I have this character idea of an assassin who is an oracle.  In discussions with a friend about the character, the character would need to be lawful evil as there would be a set of rules the character follows.  The development idea would be three levels of thief, taking assassin at 3rd level.  At 4th level, I think Cleric of the Prophecy Domain (Elminster's Candlekeep Companion - DMGuild) would be added.  I'm not sure if progression up the cleric or assassin track would be better after that.  I don't know if there is a better combination to create the character.  Thoughts?

The story in my head is this person doesn't remember anything until they are 10.  At that age, they remember being taken in by a "master thief" (thinking of the person whom Oliver Twist asks "Might I have some more?").  The character is taught the tools of the trade and allowed to join a junior guild.  When the character becomes an assassin, the gods (or some other outside entity - haven't decided) take an interest and "touch" the character going into level 4.  The character goes from being a rising start in the guild to dropping out and becoming a specialized assassin.  The character only assassinates those the gods/entity tell them to kill.  The killing can be as simple as stabbing or poisoning to as long term as looking to do something nice, like give a child a puppy, that when the puppy gets older, kills the family or giving a bouquet of flowers to someone who gets covered in pollen and triggers a lethal asthma attack in someone else.  The character doesn't question why, just gives the puppy or flowers to someone and lets nature take its course.

The rules would be:
1) Never attack someone/something unless attacked 1st.  The gods/entity wants the character to kill but only those deemed necessary to kill or in self defense.

2) When the task is given (normally through a trance like state for the character - character looks like they spaced out), the task is to be done as soon as possible.  As discovered, to not do the task leads to complications in other activities.  Therefore, it is best to leave whatever one is doing to complete what needs to be done and then return to the previous task.

3) The visions either tell who is to die, not how, or what activity to do, but not know the reason.  For example, the vision shows the face of a person.  That person needs to die.  Do it as soon and quickly as possible.  Or, the visions says take a puppy found in this alley and give the puppy to the child who bumps into you.  No reason given in either situation.  Best not to question the visions.

4) No one is safe.  The visions could target friends, family, companions, or others known to the character.  Best to act and get it over with instead of dwelling on the person.  Therefore, never form close attachments.  (Though I'm thinking John Wick thoughts with the puppy/dog.  The dog always comes back to the character no matter where the character is. Mess with the puppy/dog, ignore rule 1.)

I'm not sure if there are any other rules or ideas beyond those 4.  I'm normally a chaotic good/neutral good kind of player.  Playing lawful evil would be different.  I also realize this character would be a pain to the other party members ("Why aren't you attacking?"  "They haven't attacked me so why should I attack them?").  Last note, this is the last fun idea I've had for a character.  I'd like to make this work to start playing again.  Thanks for the ideas, suggestions, and thoughts.

As I think you've already figured out, this idea is probably better suited for an NPC than a PC. Your rule 1 is going to annoy your allies in fights, and your rule 2 could put the DM in an impossible situation -- they either have to basically ignore your backstory when constructing adventures, or have you abandon the party and go off mid-adventure if the DM does elect to have your god/whatever give you a mission that isn't just "hand some kid this puppy"

Now, there are campaigns where the backstory can be just window dressing and no one expects it to actually come up, and campaigns with looser story structures and big gaps of in-game time between sessions where you can just say you were off doing missions between the party's adventures. If that's satisfying for you, then yeah, this character could work, but your whole "god-chosen assassin" thing won't really ever come up unless the DM throws you the occasional bone of a vision of the BBEG, or maybe builds something around the consequences of one of your off-camera kills 

Mechanically, I'm not familiar with that homebrew cleric subclass, but in general rogue/cleric is an "I'm doing this for story reasons" combo rather than a "these two have some mechanical synergy" multiclass. There are probably better options for the kind of character you want -- I know a lot of folks don't even think the Assassin subclass is the best option for making an assassin character, and a god-touched character doesn't have to be a cleric at all. Gloom Stalker ranger especially might be a worth a look if you want something that fits better with cleric (both are WIS casters)

AntonSirius - Thank you for the reply.  I was afraid the character would be more NPCish than PCish.  I'll check the Gloom Stalker ranger and see if that fits the idea.  My last character story was altered significantly by the GM (the change fit the story perfectly, problem was it wasn't discussed with me ahead of time and altered my character significantly from how I was playing, I turned the character into a NPC and walked away from the game).  This idea is the only one I have that interests me to attempt to play.  The character idea is 180 degrees different from the character I walked away from and made a NPC.  Anything else, or any other game, doesn't interest me.  Therefore the hope in figuring out a way to create and play this idea.  If nothing else, I can create my own stories and have fun that way.  That might get my spark back to play other games.