My question is in the title: How long do devils (like horned devils) live?

Traditionally, devils do not age and are immortal. They could potentially live forever unless something ultimately kills them.

Important to note that a devil killed outside of the Nine Hells (i.e., Baator) doesn't actually die and eventually reforms within the hells. 

They're immortal (unless destroyed on their home plane).

Let's also remember that horned devils and the like can be transformed up and down the devil power scale as they impress or fall into disfavor with their superiors.  So immortal unless outright killed in Hell, but also very mutable.

Yes, all devils can be promoted or demoted into greater or lesser forms based on evaluation of their performance by the Infernal Bureaucracy.  In older editions, every devil was required to start out as a lemure, then work their way up the chain, but apparently in 5E that's been abandoned given the instances in Baldur's Gate: Descent Into Avernus of individuals getting promoted immediately to different forms (some of which are quite advanced).

Quote from 6thLyranGuard >>

Yes, all devils can be promoted or demoted into greater or lesser forms based on evaluation of their performance by the Infernal Bureaucracy.  In older editions, every devil was required to start out as a lemure, then work their way up the chain, but apparently in 5E that's been abandoned given the instances in Baldur's Gate: Descent Into Avernus of individuals getting promoted immediately to different forms (some of which are quite advanced).

 Though I guess there's no reason a Devil would necessarily have to keep a newly arrived soul a Lemure.  It also seems in 5e it's more a sliding abacus than a rungs on a ladder.  Asmoedeus could make a pit fiend a lemure or vice versa if he wanted.

Technically yes, but devils are the race of lawful evil.  They're supposed to be the epitome of following rules, not making exceptions- that's the chaotic thing to do.  The Nine Hells are the place where you're expected to follow orders even if a tiny exception could be more efficient.  You're not allowed to think for yourself unless you have the proper paperwork signed in triplicate, sent in, sent back, queried, lost, found, subjected to public enquiry, lost again, and finally buried in soft peat for three months and recycled as firelighters.  A Nine Hells where they can treat the rules as if they're mere guidelines misses the point.

Devils are lawful evil, but that does not mean any nicer than CE demons.

Quote from 6thLyranGuard >>

  In older editions, every devil was required to start out as a lemure, then work their way up the chain, but apparently in 5E that's been abandoned given the instances in Baldur's Gate: Descent Into Avernus of individuals getting promoted immediately to different forms (some of which are quite advanced).

 This is generally the result of a specific pact request, or a reward for being a devout follower of Asmodeus as a god (and Asmodeus makes the rules). Going non-lemure is supposed to be an exception rather than rule, but that's because devils are stingy (higher forms require a small drain on the Hell's divine power reserves to manifest) and dont like rivals, rather than it being against a cosmic law.

If anything, given that LG gods can ascend anyone to be an angel, it's a part of the cosmic rules.

Noice.

Quote from 6thLyranGuard >>

Technically yes, but devils are the race of lawful evil.  They're supposed to be the epitome of following rules, not making exceptions- that's the chaotic thing to do.  The Nine Hells are the place where you're expected to follow orders even if a tiny exception could be more efficient.  You're not allowed to think for yourself unless you have the proper paperwork signed in triplicate, sent in, sent back, queried, lost, found, subjected to public enquiry, lost again, and finally buried in soft peat for three months and recycled as firelighters.  A Nine Hells where they can treat the rules as if they're mere guidelines misses the point.

That I think over weighs the influence of The Screwtape Letters in Hell.  You can have a Lawful Evil moral calculus that's something more than an infernal pyramid scheme of grade chasing.  I feel especially present lore suggests devils are more min/maxers than complete subscribers of some sort of incremental chain of being.  Avernus in particular is a war zone where chaos is constantly making incursions, the effects of which are fluid battlefield promotions and reassignments (having worked for a giant government "duties as assigned" was the most precarious part of job description verbiage).  Avernus itself is broken and doesn't function at all per its initial design (a paradise of temptation), the idea that the Blood War has impacted the Nine Hells in such a way that the incrementalist hierarchical assumptions alleged to be in its infrastructure is actually kinda dramatic irony.  

Devils are selfish and ambitious and they will exploit rules.  Exploits don't mean breaking it means maximizing one's advantage (again like a mix/maxer) as seen in all their dealings.  One step at a time ... I know that's a AD&D and probably subsequent editions thing, but I think it discounts what diabolism and turns the Hells may denizens into evil Modrons, and that's a simplication if not lobotimzation of lawful evil.

They're not evil modrons, but they're supposed to embody everything that's evil about bureaucracy.  All the waste, the inefficiency, the destruction of the individual.  And none of that really seems to be getting done any more.

Quote from 6thLyranGuard >>

They're not evil modrons, but they're supposed to embody everything that's evil about bureaucracy.  All the waste, the inefficiency, the destruction of the individual.  And none of that really seems to be getting done any more.

 waste and inefficiency isn't evil...its incompetent.  A bureaucracy doesn't have to be incompetent to be evil, and in fact, I would argue that Devils represent a very competent bureaucracy; one in which everything runs the way it should be, just to evil ends (The DMV isn't evil, just frustrating due to the incompetence of their organization...Devils are more like the Nazis...the Nazis were evil, and did reprehensible things, but they weren't exactly known for being incompetent at doing them...if their organizational skill had been less competent, the scale of their atrocities would have certainly been a lot less).

In a competent bureaucracy, an individuals talents would be recognized and their assignment suited to them...so an evil general could start as a horned devil or pit fiend, while a petty criminal with limited skill/intelligence would become a lemure, each according to their ability.

Quote from iconarising >>

Quote from 6thLyranGuard >>

They're not evil modrons, but they're supposed to embody everything that's evil about bureaucracy.  All the waste, the inefficiency, the destruction of the individual.  And none of that really seems to be getting done any more.

 waste and inefficiency isn't evil...its incompetent.  A bureaucracy doesn't have to be incompetent to be evil, and in fact, I would argue that Devils represent a very competent bureaucracy; one in which everything runs the way it should be, just to evil ends (The DMV isn't evil, just frustrating due to the incompetence of their organization...Devils are more like the Nazis...the Nazis were evil, and did reprehensible things, but they weren't exactly known for being incompetent at doing them...if their organizational skill had been less competent, the scale of their atrocities would have certainly been a lot less).

Actually, the Nazis were quite incompetent and extremely inefficient.  As Linkara put it in his review of Secret Empire:

[The story] kind of bought into the greatest lie that fascists ever told: that it is strong. That it is orderly. That it is might and power and deference to might and power. For the longest time, the popular belief about Nazi Germany was that it was an efficient war machine that took a broken people and almost conquered the world. The truth is, the methods they used were inefficient, corrupt, and ultimately self-defeating. They cared more about propaganda and pushing out an image of fortitude than actually doing anything that would truly help themselves. They used scapegoats, bigotry, anything they could to try to get people on board with the programs, even while they suffered under them.

And the same thing originally applied to devils.  The propaganda that they were superior to demons in any way was just that, propaganda.  They were not a necessary evil to save the multiverse from demonkind.  They were just as bad, only in a different way.  They were simply another flavor of evil fighting over which flavor of evil cola everyone was going to be forced to drink.