My party just arrived in the Gnome city of Tinkertown. The city is set in tiers that rise up the side of a cliff, the manufacturing tier has been taken over by rogue automatons. My idea is that the head tinker/artificer of a factory has gone crazy. I don't have all the details, I am thinking maybe he got ahold of an ancient relic and fused it with himself, but am open to suggestions. The relic will have given him knowledge to make better machines. The stat block I am using for him is an 8th level artificer with increased hp. I would like some ideas for lair actions when the group finally finds him in the back of the manufacturing tier, ideally they will have had several encounters with drones and maybe some homebrewed clockwork soldiers. The boss will be using guns taken from the Explorer's Guide to Wildemount. The party is 4 adventurers at level 5. Any help would be appreciated.

Humanoid NPC in the monster stats look to typically be able to cast a free spell, w/out using a spell slot as lair actions on specific initiative count.  So if looking to base your lair action upon official monster stats it's not a bad place to start. Otherwise, having 2d6 small mechanoids roll out of a box in a specific 30 ft area to force a str or Dex save or fall prone / become restrained also would fit the scheme. And/or electrical outlets (*d&d equivalent) create an arc of lightning to anyone within 30 ft of certain walls or columns. Or, reinforcements of mechanomen arrive (fiddle with undead or construct monster types as appropriate) as a possibility.

I also have zero knowledge of what artificers actually do, so I'm confident someone with awareness can provide beter suggestions.

I think lair actions are super useful for terrain management. For instance a lair action that does a knockdown in a radius... or makes all terrain in the area "difficult terrain"... or causes darkness in a certain radius. You can do that for anyone, not just artificers... and they help the boss control the battlefield.

For a manufacturing area... maybe he could spill oil all over the place, making the surface slick... or maybe he could run a bunch of machines at once, making all concentration checks rolled at disadvantage... that kind of thing.

I always like creating more action economy for the minions. I’d probably use lair actions to reanimate fallen automatons and/or give his automatons more actions. Consider giving him and his minions some cool defensive reactions and bonus actions fit nicely with this. They could be able to self-destruct, become grappling traps, etc. I used a terminator style ability to keep going in a lesser fashion as the basis for a construct to some success.  The idea is that that they are facing him through his automatons rather than facing him directly. 

I just had an interesting idea that might throw the players for a loop: the automatons don’t roll for initiative and are entirely controlled by the artificer through his/her actions, lair actions, reactions, and bonus actions. The party would have no knowledge of which ones are going next or even when. Couple that with varied abilities that are tactically interesting such as anti-magic effects, grappling, terrain impediments, sensory effects (blind, deaf) and you have an encounter that might be a puzzle as much as a combat. 

I think it’d be cool if the relic is something that allowed the tinker to fuse themself with machines, kinda turning themself into a construct. Lair action: a new piece of equipment fuses with the tinker. You know those fights that have multiple phases, you think you killed them but then they reanimate as something else and the second half of the battle begins? It could be a different take on that. You have the tinker in their human form, and the tinker in their full construct form BUT they are fighting them as they are transforming. Each time a new piece of equipment is added they gain some HP and by the time 5+ rounds has passed they are fighting a machine infused artificer. Just pick an official construct from the monster list and slowly add abilities and incremental hp equivalent to the chosen monster.
This might be one of those things that only makes sense in my own head, but if for some reason I did manage to properly convey my idea, it could be pretty cool.

other than that, I’d look through the construct monsters and get some ideas for lair actions or other effects from the monsters abilities, readjust to scale for monsters of appropriate level if necessary. Have machines and stuff around the battlefield that are the source of the effects. Maybe like a roomba that randomly moves around the battlefield and releases a random random effect on the lair’s turn. Example: Noxious gas, explosive wave of force damage, electrical shock (paralysis or stun), grease. Roll a d4 to see which occurs