Is it possible to make your own tyre skins in LFS?

You can edit the dds file which defines what the tyre will look like (Tread) and also the sidewalls. People have made some nice tyres textures just do a search. If you want to edit your own you will need a picture editing software and a dds converter

It is important to note than only you will see your modification, though. Other players online will see whatever texture they have installed, not the one you have installed.