If I'm correct the Lapis Cross is a key item that's obtained for your promotion isn't it? If so you need to talk to him (Don't choose the option that gives the quest.) and select the option to apply for a promotion. Providing you have the seals available you should be told you have to prove your worth before he'll give you it. That should trigger the quest I believe. I might be wrong there and you can purchase it without triggering the quest but applying for a promotion should give you the Lapis Cross.