The purpose of spying on the meeting was not to gain information on the current situation, although that was definitely helpful in its own way. No, the purpose was to wait for someone who was based out of London. That way he could ask them about Belle.
Of course he would not do so using his identity as the Innkeeper, but as Leo. That way he still had a connection to the Inn, meaning they were more likely to pay attention to him. If he just showed up as Lex, it was unlikely anyone would give him the time of day, considering they had their plates full.
While everyone waited for Marlo's report on the aliens, the meeting continued. They were mostly discussing defensive measures and troop movements, things that were of little importance to Lex. But there was one discovery that improved the mood.