Dropped is accurate and her holding it implies she picked it up for him. Lost can work, but to me would more so imply that it's gone for good or that its whereabouts are unknown. I'd go with dropped.
I hope and think there won't be any weird drama, but the author could throw a joke in about kidnapping. Meh
Honestly, I'm giving the author props in this chapter purely for having a realistic stair catch happen instead of a MC dashing down half a stair case in the time it takes for their love interest to start slipping.