How do I make a persistent USB drive or a manual install to s USB drive
I’ll refer you to this answer on persistent live systems
It contains links to the Ubuntu wiki page too.
If you have questions, you can leave them here, as @sudodus is a member and maintainer of the
mkusb tool I’d use if I was creating one.
As for installing Lubuntu, you didn’t specify a release so I tried a day old groovy ISO and it wasn’t readily apparent how to install to a thumb-drive I inserted, however when I booted a Lubuntu 18.04.5 system, in the something else option I found it easy to locate the second thumb-drive I wanted to install to, though I did use commands
lsblk mount |grep sd
to detect which thumb-drive had the live system I was using, and which was where I’d install to.