Lucchini made it back to the Chalice for a few reasons, to get her things and see if Shirley wanted to stay or go with her. There was no way she was going to leave her home with the damages, not when they could use her there to help fix things.
But first.... she had to ask Mio for leave.
"Major? I... I'd like to request leave. I can't leave them like this, even though damage was minimal... I have to stay to help rebuild the damaged part of the city."
Lucchini's got her gear packed up, still debating if she should take her strikers or not. She's sitting in the hangar closing her eyes.