How to cover a deep freezer lid that is rusting?

You could put some decorative Contac paper over it if you don't want to paint.

You could clean off the rust and attach contact paper instead of painting.

I would lightly sand the rust spots to get rid of them. Then Spray with Rustoleum spray paint in the color of your choice. It should last for years using Rustoleum.. If you have stencils you can spray paint using the stencils for design if you do not want to paint the entire freezer.

I would cover it with removable wallpaper and make it pretty. Target has some cute, affordable designs.

Yep. Lightly sand to remove the rust and roughen the surface for paint. Use Rustoleum appliance spray paint. Several light coats will give you a smooth finish

probably easier to paint it than cut something to cover it nicely and it be moisture resistant rust will continue to spread if you don't get rid of it so you need to sand it anyway then spray paint it see William's post

I painted the top than applied contact glue and covered with pallet wood.. looks great, and has been going good for the past few years so far.