Any way to do a lattice fence without digging posts?

I have a dog run in part of my back yard, she's older and not gonna jump over anything now so I'm looking to replace the wire fence that was destroyed when we had my trees cut.

I was thinking some 3' lattice fence would look ok and be reasonably priced. I really don't want to dig 5-6 fence posts though as there's roots all over my back yard from the huge oak trees.

Is there any way to run a lattice fence without setting posts in the ground?