If cross' inconvenient skill sets become the counter for that Lich, I will drop this series. I'm not buying for such cheap plot armor.
To be fair, Aegis Shot seems like a decent counter, if only because of being an error skill with a defense-pierce/defense-reduction type of effect.
After all, he doesn't gain immunity, only strong resistance. And if he's resistant to debuffs because of being magic, a skill whose literal entire point is being a cheat-y kind of skill, and as such bypassing the conditions for the lich to shrug the attack off, would likely combo well into Rione using one of her skills to finish him in the vulnerability window.
As someone who has played games where you have to use that kind of strategies to beat some enemies, it seems reasonable to me. And Cross HAS to land a counter to throw Aegis Shot regardless, so not really easy nor safe to perform.