When Lon and Luci are going to split up the assets, he only wants his pet lizard. While this could be taken as a sign of maturity and true love for Luci, as he is going to give everything to her, it is actually further proof of his immaturity. He is unwilling to go through the list of assets to split anything. After saying he wants his lizard, he basically shuts down. He does not say anything else in the scene, even after the lawyer asks what Archimedes, the name of his lizard, is. Lon forces his wife to answer the question. This shows his overall lack of maturity.
Lon is also not a true adult because he shows a lack of respect for others. Lon makes that snide comment about believing what you want and he refuses to look at the list of everything that the two of them had to split. This shows a lack of respect for the effort which Luci had put into that list because while she had cataloged everything so they could decide which of them needed the item, Lon will not look at it. He cares only about himself and his lizard. He refuses to engage in a meaningful, adult conversation with Luci and the attorney, instead shutting down and refusing to