Well, specifically for the example at hand... as all of these kinds of things must be case-by-case...
A LG cleric who burned down an orphanage.
Was the orphanage filled with undead/vampiric/ghoul/zombie children? Then it's fine.
If the orphanage was housing some great evil, but all of the normal innocent children and staff had been evacuatede? Fine. It's a buildingit can be rebuilt. Destorying the evil in the fire is what was more important. The LG character could/might very well EARN some inspiration by sticking aorund and assisting, either in coin or labor if not both, in rebuilding the orphanage.
If they just burned down an orphanage (or tavern or castle or, doesn't really matter what the building is) with Innocent people (whether they are good or not is equally immaterial, as long as they're innocent) in it? Then I'd say "anti-inspiration" is the least of this character's problems. Lowkey is correct, however, that the onus is on the DM to handle this, not the other players.
Immediate and possibly irreversible, channeling divinity, and (in 5e) Divine Interference are completely and immediately off the table. Healing spells? Hell, I'd say ALL spellcasting goes unanswered until some form of atonement is made...and even then, they can have some 1st level spells until I have seen they are serious.
This, of course, comes with an immediate and permanent until proven otherwise alignment shift out of LG to...N...unless, of course, it was sheer psychopathy in which case, do not pass go and go directly CE...which, in itself, may mean the cleric NEVER gets their magic back if they can't return themselves (many months if not years of RP time showing consistent behavioral standards and multiple atonement spells and/or serious, risky, nigh impossible quests) to a stable LG alignment. Otherwise, more likely, the player will say, fine, f**this, I'll get a Neutral Deity...and, basically, only a CN deity will want someone who goes around torching orphanages, and/or any Evil deity is going to be interested in taking up a fallen/former LG soul.
Doling out "anti-inspiration"...not really a thing, nor a player's place. If a LG cleric burned down an orphanage with innocent children in it and deaths occurred, and there was no big evil thing that was stopped in the process...like major, HUGE evil thing...completely destroyed/stopped...the DM should [had better] come down like a divine hammer of wrath and judgement on this pathetic mortal's body and soul.
If you're going to use alignment in the game, then it damn well better be USED! And something like this? Immediate DM-originating change to that cleric's character sheet and whole world.