Since only the old man from before named Hugo was against Lux joining them and the other didn't say a thing, he was allowed to join the expedition.
The others weren't that concerned about the rewards, as they were about Khione's impression of them.
She personally picked and brought Lux here, so he wasn't a random person joining them, but an important figure they never heard of before.
Not to mention the rumors a week ago about their princess carrying someone in her arms to reach the Divine Pool, and her return along with some humans from a faraway land.
These things added together made most of them believe that the human before them, despite only releasing a God Class power level, was actually an important person to Princess Khione.
They weren't as dumb as Hugo to reject him joining their group.