He needs to show hard evidence the sex worker he "dated" was in fact really dating.
No, none of that is necessary.
Simply the fact he admitted on camera he 'dated' a sex worker is more than enough proof that someone stating 'he engaged in sex work' is a reasonable conclusion.
Dating a sex worker is engaging in sex work. The argument isn't "in which hole did he put which parts of his body?"
Did he go to Thailand? Yes, admitted.
Did he meet sex worker(s)? Yes, admitted.
Did he use a sex workers services? Yes, admitted.
It is reasonable to conclude, and state as fact, that he engaged in sex work while in thailand.
Lloyd thinks he can be pedantic about where his penis went. But no, that isn't necessary.