I'm a cleric that will take the church inquisitor prestige class, but I am wondering if the church inquisitor levels will stack with my cleric levels for the Lust domain’s granted power, or if only my two cleric levels will count.
Domain Granted Powers
Not by default. When domains specify “cleric level” and you get them through the cleric class, then they mean just your class levels in cleric. A prestige class that advances cleric spellcasting, like church inquisitor, does not count for domain granted powers, because
He does not, however, gain any other benefit a character of that class would have gained
Since your cleric level for domains is not caster level, spells per day, or spells known, this spellcasting feature does nothing for it.
A prestige class can say it counts as cleric levels for the purposes of domain granted abilities. Church inquisitor, however, does not do so.
Complete Divine has a confusing section about “extra domains” that goes into great detail about how the domain spells work when the domain comes from a prestige class—how that affects clerics, how that affects other prepared spellcasters like druids, how that affects wizards specifically due to the spellbook, and how that affects spontaneous spellcasters. It addresses how those spells are still arcane for arcane spellcasters.
But on the subject of the granted power, it is quite brief:
If a noncleric enters a prestige class that allows access to a domain, the character still gains access to the domain. She can use the granted power bestowed by the domain normally.
What does “normally” mean for a noncleric with a domain that references a nonexistent cleric level? No idea! The rules don’t say whether you’re supposed to pick a class, or use the same class you’re advancing the spellcasting of, or that you should just use your entire character level—any of these might make sense, but it doesn’t specify at all.
Just in case there was some confusion here: as you continue to advance your cleric spellcasting, that includes gaining new domain spell slots from which you may prepare your domain spells.