To improve his PR in the village, esp. her family who are big guns maybe?
The Justin we know is worth more than the lot of them put together so it's highly unlikely that he's interested in trying to impress them.
I believe in Justin's relationship with Lillian. She's not of any particular use to him from a business point of view so I can only assume he's very taken with her. His divorce is going to cost him a pretty penny so what other motivation could there be, if not simply a desire to be with her?
Obviously he'd prefer to be accepted by all the family but, hard-nosed businessman that he is, he didn't consider the ramifications of his offer on Lillian and Tony's relationship.