Well, if LiLi is suppose to grab Windows users...
I would say a nice Solitaire game 
I guess there is not much say why
Aisleriot could be a bad choice, so perhaps, but...
Certainly it needs to be a very lightweight piece of software.
It needs to be simply playable, have pleasant aesthetics.
It must have system specifications that would allow it to run even on 'resurrected machines'.
Plus,
Aisleriot is quite symbolic for the PC world altogether, so I guess...
But what I thought is that
VVVVVV: Make and Play Edition - link
HERE - created by Terry Cavanagh, the maker of
Super Hexagon, would look very nice on Linux Lite. The problem is, it is a proprietary title. Another problem is, even though there are available over the Internet some well rated player-made levels, the installation of these could pose a problem to casual users and I doubt whether having any of those levels preinstalled on the OS along with the game, would legally be safe.
EDIT:
VVVVVV: Make and Play Edition also is not on the repo, so deleting it would be kind of irreversible. Kind of.
