If you really like the black lattice, why not hang it horizontally like a big picture and attach some black pots to the lattice to grow some plants? If you get a good amount of sun there, you could even grow some herbs.
Even if it's shady though I'd stay away from ivy. It's like inviting rats to couch surf at your place. I would do something unexpected and easy to manage like ferns.
Or you could just leave the lattice for visual interest-no plants. If you leave it blank, you could tack a sheet to it, borrow a projector and have outdoor movie and picnic nights in the summer.
If you do attach something to your house, make sure you create enough of a gap for good airflow. I can tell you from experience that rotten siding is neither cheap nor fun to deal with.