Near the end of Episode 9 after Kirito killed The Gleam Eyes, he's complaining about how he can't go back to his place because everyone is hounding him about his Dual Wield Skill, Liz then shows up saying
It was our little secret until you blabbed about it
Implying that she knew about his Dual Wield before hand, however when Kirito got Liz to commission his second sword she never asked what it was for. Considering that Kirito was hiding his Dual Wield and it didn't come out until the boss battle how did Liz find out?