She wasn't familiar enough with Kane and the others to know their specific situations, so she didn't know whose vehicle this was, or if it was shared squad property.
As for why she thought it wasn't purchased, it was because Funa hadn't heard of such a vehicle.
Upon hearing Funa's question, Lilulu immediately said, "It's Kane, oh, he's the best at making these mechanical things."
The one in the whole squad who loved Kane's mechanical creations the most was Lilulu.
Whenever Kane had a new invention or creation, Lilulu would always be the first to try it out and want to control it herself.
If it was some small mechanical toy, she would even ask Kane to make a physical one for her.
So now, in Lilulu's space equipment, there's a corner specifically for storing various mechanical toys Kane made for her.
