Four minutes. The cave only lasted for four minutes, and in that time Lex did his best to blindly memorise every interaction the crystalline eyes had with the surrounding laws. The issue was that the interaction was with foreign laws that he didn't understand too well, so deciphering what was happening would not be easy.
He also looked through the corpse's memories, but as it turned out the memories had a halflife, meaning that the corpse would lose its older memories in repeated intervals. Thus, what Lex saw was less of the beings regular actions, and more of how across the ages the surrounding laws reacted to the gaze.
While Lex himself didn't get the answer, at least he got a lot of information from which he could figure out the answer on his own. It was good enough, given the circumstances.
