Quote from Beardsinger >>

You’re the DM? Absolutely. Kill em all. Show no mercy. They will see the weakness in your eyes. Roll the dice and play it as they fall.

 See, but that's not what OP was saying. They don't want to play the dice as they fall, they want to have the NPC die no matter what the dice say.

As some others have said, you need to be careful about forced narratives. If the party thinks they can affect this outcome - and that's generally a reasonable assumption in D&D - then they will push back, and often this results in the DM somewhat ham-fistedly bending rules so that the thing they want to happen does happen. That just doesn't feel like a good game to anyone.

I handle "railroad scenes" like this either offscreen or in a "cutscene" where it's clear the party can't change the outcome.

Or better yet, actually play the dice as they fall. Put the NPC into a terrible, deadly situation and give the PCs a chance to pull it off. Sometimes the players throwing a wrench in the narrative turns into an opportunity to blaze a new trail back to your goal. That's part of the fun of DMing - you're not telling a story to a passive audience, you're enabling the group to tell a story as you go.

I think it's fair for the DM to attempt to kill off the NPC. However, if the party finds some way to miraculously save that ally, then there's no saying that the NPC should suddenly drop dead of I-no-longer-need-him-in-this-campaign-itis. Make it a challenge to save the NPC. If the players put in the effort to save his life, then let his life be saved. Of course, there's no saying that he can't wind up getting injured, with his adventuring days getting cut short, but that's up to the dice rolls and the player actions to determine.

This last option especially helps should you wind up with a situation where, in hindsight, the NPC was still far more useful to the story than you gave him credit for. If the NPC only wound up getting crippled by a blow to the shin, maybe he returns after a few bouts of restoration from the local Clerics, or he shows back up with a peg leg and a few cool scars. It's much easier to write that style of return, than it is to explain how the guy who got smashed under a boulder suddenly joined back up with the party, like nothing happened.

If you have a justifiable reason that makes sense.  You can have at it.  As the dm, you're incharge of moving the world.  With or without your players interacting with it.  A village will be raided by goblins without the players input.  A politician will steal and election without the players input.  Its a co-operative story telling. Adventure.  The players can and will make the story with.  But as the dm, its ultimately up to you what happens in response to player actions.  If the players can have a say in what happens to monster, baddies, or npcs.  Your job is pretty much pointless.  

Read the room.  See if it's a good idea.  But good or bad things happen in dnd based on rolls or actions.  And it's something that players (which includes the dm) have to square with.  

Hope this helps. 

It's 100% fair for the GM to kill any NPC. The trouble is, if the PC's really care about their friend, it's unlikely they stay dead for long. So you might need some fairly spectacular killing. Dissolved by a gelatinous cube, plane shifted to Elemental plane of Fire, eaten by Father Dagon as a sacrifice. 

Otherwise, death quickly becomes a minor, temporary inconvenience. As I'm sure others have said, btw.

If you intend to kill off the NPC, consider the narrative. It will be weird if you try to single the NPC out in a fight, so just let the fight run as usual. If NPC dies from bad rolls and such, let it be, just don't make it intentional for no reason. 

Accidents do happen, so you might just use that. Soil erosion, lightning strikes, or getting bitten by a black widow and not noticing it...Allergies too can be deadly.

Another way to do that, just let the NPC leave the party for a different issue. One reason a DM has used is that the NPC has finally located her enemy and she will be leaving for vengeance. Our characters have interacted with her enough so she shared her story with the group and we knew she will be leaving if she found the enemy. That's a way to do it, but it requires you setting up that prior.

Now all those are alternatives I have seen before, but if I were the DM, here is what I will go through before making that decision:

A. Take note of how your players use the NPC, let's say the NPC is Gary for easy reference -

     1. If they are using Gary as a tank, let the group get some items that make them tanky. Make those items uniquely inaccessible for Gary.

     2. If they are using Gary as a healer, let the group get easier access to healing items/potions.

     3. If they are using Gary for skill check and such, well, maybe Gary is a little bit overpowered? Perhaps offer items to the group where they can get advantage for doing certain skill check/lower the DC so players can get comfortable in rolling.

     The sooner they are relying less of what Gary can offer, the sooner they find Gary not essential for their adventure, and easier for Gary to go off somewhere else and enjoy his life! Gary exits stage left and goes off for a brighter future. The same goes for that NPC I mentioned, we were players down so our group hired a follower. We made it till the end of the campaign and we recruited new players for the next one, so logical for the NPC to leave for her vengeance as she has completed her mission/goal of the DM (filling in a slot).

B. Reflect upon how you have setup the mood of the campaign -

    If the campaign is always sunshine and vivid, a grim death is going to hit the group hard. In that case, I would send the NPC off to a brighter future (probably got married and settled, but it would be weird if you force it to happen all of a sudden, so at least plan ahead). If the campaign is filled with deaths, then it will be fine that the NPC got killed in a battle or by a trap or in an accident. You did warn them of the dangers ahead and death will eventually come.

C. The possibility of revival? -

    If you are killing off the NPC, does the group have access to revive the NPC? If you want permanent death, you might consider dying naturally to old age as a way to do it. Furthermore, in your setting, do you have revival service in certain locations? This factor alone can terminate your plan of ending Gary's life as an NPC. Also, is Wish spell allowed in your campaign? Does the group have access to it? There are plenty of ways to revive a character, so watch out.

D. Is the death necessary? -

    If you are trying to motivate your players to take certain actions against a force of evil/good (depending on how you want it to go), sure, a death of a dear friend will definitely be a solid way to push them over the edge. The question is: is it necessary? By all means, if the group is already on the course, the death is not necessary. If you find Gary too overpowered, find ways to shut him down, like the article on DnDBeyond said, give him a cursed item, give him a level of exhaustion, make him crippled from a serious injury. There are tons of memes (pun intended) you can use to drag Gary down to the mortal realm of man. After all, if death is the only way, let it be worthy. Let that weight sink in for the drama. Let the players grief for their loss. Give them downtime to go through the trauma. Let them roleplay the greatest tragedy you can offer. Then, make those magical moments a part of the remarkable journey you have brought to them.

E. Handling the grief -

     Everyone handles it differently. Some just shake it off. Some will go silent mode. Some will talk it out. So make sure you give players time to grief. Most DMs waste no time moving on with the campaign/plot, but you can do it better by giving time to players to grief in roleplay. What makes certain campaigns more memorable than others is that we are emotionally attached to it. There are high highs and there are low lows, but emotion is the key to making an impressive campaign, either it is a comical relief, a silence of sadness, a burst of rage or a brilliant line in the heat of the moment, those are the sparks that make a campaign unique and memorable. Be thorough in your decision making, don't let the death be compulsory if it is meaningless and it doesn't offer values to both the players and you, a DM. 

~~~A sample of death in battle~~~

Gary tries to cast Healing Words, soon as he mutters those holy prayers, an arrow hits him in the head from a corner. "A follower of (insert your deity name here)? How dare you come here and utter those unholy phrases."

It's a crit, Gary takes 15 points of piercing damage. Gary was at 3 HP...the arrow pierces through his skull and he drops immediately.

~~~End of Gary~~~

~~~Death by accident~~~ (assuming everyone rolls bad prior to this)

The herd of cows is charging full speed ahead and Gary isn't fast enough to get out the way, neither is X/Y/Z (players) quick/strong enough to pull Gary out of harm's way. 

Gary is run down and trampled by the herd of raging cows...he takes 75 points of bludgeoning damage and he is on the ground, motionless.

~~~End of Gary~~~

Always remember: a great campaign is a masterwork from both players and DMs. So if you are going to pull it off, make sure it is a worthy one that leaves a mark.

Pretty sure that death by a herd of cows will be a meaningless and ridiculous death that will be remembered as a meme. And a perfect demonstration why death by accident will always be the last resort.

(Death by falling into a toilet is real...but that will be another meme for another day)

If it helps/fits the story - absolutely! (Been there, done that, repeatedly)

Obviously I am not saying wipe them all out, but experiencing loss is a part of the game and can prove to be a powerful motivator (avenging the death of a loved one, etc.). It also goes to reinforce the notion that mortality is a thing.