I didn't make it!
I placed the bust in the cupboard, went to talk to Lex and when he didn't believe me, I went to a different quest. Now that I'm ready to convince Lex, I can't find him. When I activate the quest, the map in my inventory points me to a place in the waterfront that is literally in the water, and my in game guide map guides me to back to the city in the rich neighborhood.
When I enter the neighborhood, the guide arrow turns green, but points directly at the wall, and Lex is nowhere to be found. When I'm in the temple district I think, my guide arrow turns green and points directly at the wall. I have scoured the guard barracks, and still no Lex. When I look at my world map though, it is marked in the waterfront, in the water, but only turns green when I am in the temple district.