yes! make the lean-to come off the back fence. make note of where the wind is coming from at various times of the day. I use weather underground (wunderground.com) to see this at a glance. You could frame it, use t-posts, etc.
Is the wood slat fence sturdy enough to build off of, using it as one of the walls?
Temporary, emergency type ideas are:
Pound 4 t-posts into the ground (or 2 if you can use the fence as the back wall)
Run 2x4 non climb fence and hardware cloth around the posts to make a perimeter.
Brackets and...