Dealer did not put enough oil in car?

The dealer did not put enough oil into my boyfriend’s 350z however he did not realize this until he changed the oil himself the next time. He has changed it before so he knows how fast the oil burns and it should not have burned through that quickly. There is now a ticking noise due to not enough lubrication on the lifter. The problem is, he did not document how much oil he drained or anything like that and the ticking did not come on right away, so it is now being dealt with a lot later.

My question is, is there any way to get the dealer to replace the lifter for free because it was due to their mistake? Is there anyway he could prove this? The car is a 2005 so it is no longer under warranty unfortunately.