There was no way Lex was going to call himself the Innkeeper, even in a situation where he was sure he was going to win. The universe was full of things he couldn't even imagine, so unless he was in the well-protected environment of the Inn, he was going to make no claims to that position.
Within the new hell that Lex had created under the name of the Abaddon Inn, Lex studied the Gon race member, analysing every single thought that went through his mind.
In truth, he had not teleported them anywhere. Instead, Lex had used all his recent experiences and amalgamated them into one of the most potent tools he could imagine - one that was even more devastating than pure, brute strength.