Lysandra was surprised by Shane's sudden offer. She simply wanted to challenge Shane because among her set of Survivor Skills, it included Combat Sense, which allowed her to notice Shane's strong combat ability.
This Combat Sense didn't just help her during combat but also in assessing other people's abilities. In short, she knew whether she had a chance of winning against her opponent or not. This was the main reason why she had chosen Shane to teach her or at least show her how much more she could improve.
Just from the moment she saw Shane, she knew that he was the right person for the task.
Of course, she also had another Skill called Survival Instinct that she had obtained after being critically injured once and surviving it.
In total, she had obtained 5 Survivor Skills after being in so many life and death situations… However, Shane's combat ability was still several times higher than hers.