I've been struggling to see a use case for building Lucifer rather than Cerberus.
First, looking at the pros and cons of Cerberus vs Lucifer
Pro: 50% greater range (>2x area covered)
Pro: Can be buried for defence
Con: Half the single target DPS
Con: Slightly more expensive
Con: Less accurate
Con: A bit more fragile
Seems ok, right?
But when would you want what Lucifer offers?
The roles a heavy turret can take are
Stopping assaults by:
A mid weight army
Pushing the enemy back
Taking out high value targets
So how do Cerberus and Lucifer do?
In practice the AoE and extra range mean that a Cerberus will do more damage to assaulting medium weight units than a Lucifer. This gets even more lopsided when considering that both will mostly be firing at radar dots, with a Cerberus doing 3x or more damage.
Even a group of 6 Minotaurs takes about 50% more damage from a Cerberus.
What about heavy units? Well, for striders, scorps and ultis are cloaked, merlin outranges the Lucifer(!), Funnelweb is a joke, Paladin is too tough to snipe and can just move in and out of range, repairing at will (in fact, due to greater range difference the Cerb will do much more damage). So it's just Detriment and Dante amongst the striders where Lucifer might make a difference (and against a Detriment not even that much of one due to only having 400 elmo more range than the Obliteration Blaster, not that a few Lucifers will do anything to a detri anyway...). What about Demistriders? Well, monospamming Grizzlies take more damage from a Cerberus (and their escorts take MUCH more damage), so it's basically Cyclops and Jugglenaught that it might work better against (and given Cyclops has terrible DPS and Juggles can't attack turrets, neither are something you need a heavy turret for).
Against shieldballs you'd think the higher DPS of the Lucifer would make a big difference, but in practice the greater range and mild shield penetrating properties of the Cerberus makes it the better choice against almost all shieldball compositions. Particularly as, once the shield is penetrated, the Cerberus AoE is devastating.
And for area denial something with greater range and able to hit radar dots (or even be blind fired) is MUCH better.
For sniping there are three circumstances to consider, units in vision, units as radar dots and buildings:
Radar dots are a clear win for Cerberus.
Buildings don't move, so the longer range of the Cerberus makes it the better option (you're very unlikely to see a missile silo or fusion in Lucifer range, but you'll occasionally see one in Cerberus range).
Units in visual range are better sniped by the Lucifer, but how many can actually be efficiently killed by it? Lances, Impalers and Emissaries are taken care of just fine by the AoE (and indeed, a Cerebrus shot can kill several). Merlins outrange a Lucifer (and, notably, NOT a Cerberus!). The only good snipe target is a commander, but these will rarely be alive, exposed and unupgraded by the time a Lucifer could be built.
So Lucifer has a couple of use cases then?
Sniping commanders and killing Jugglenaughts are somewhat niche, but why would you build a Lucifer for that? The Lance is superior to it for anything you could want!
With greater burst per cost, cloakability and the ability to move in and out of range a pair of lances are better than a Lucifer in every conceivable circumstance (this isn't strictly true, a buried tremor or snipers on a fixed front would make the Lucifer better than a Lance, but in those cases the Cerberus is far superior to the Lucifer).
Isn't the Lucifer's extra hp a factor?
Not really, if a bunch of ravagers get close enough to target it it's probably dead either way and both take 2 tac missiles to kill, while fragile arti struggles to approach a Cerberus.
So what could be done?
Making Lucifer cheaper or longer ranged would worsen the WW1 feel of a lobsterpot, so I'd instead up the damage per shot to 8000 (this requires a change in beam appearance though, can't have two identical weapon visuals with one dealing 2x of the other), making it lethal to demistriders.
An increase in fire rate is another alternative, though one that does slightly increase the trench warfare.