Lex already knows that Clark is Superman and the main point of his plan is to have Superman and Batman fight to the death. He was excited that his two combatants were meeting face-to-face.
It is made clear about two-thirds of the way through the film that Lex Luthor has been running extensive surveillance on meta-humans such as Wonder Woman and Flash for years, and that he knows Superman's secret identity.
Lex explicitly admits that his plan was to have Batman and Superman combat one another. He had been manipulating Bruce Wayne for some time. To ensure Superman would fight, Lex captured Martha Kent, and this relied on Lex knowing Superman's actual identity.
You ask, "Why does Lex give a monkeys about him? For that matter, why was he even invited to the party?" Lex wanted the two men to meet and rile one another up. He either explicitly gave Clark a press pass to the event, and was thrilled his plan was working, or was pleasantly surprised that the Daily Planet had sent Kent, which brought Clark and Bruce face-to-face more quickly than he expected.