I just hung a lattice inside. I would like to buy a plant that could climb up the lattice. The lattice is on a north wall. It will receive some indirect light from a western window, but not that much. I would prefer a plant that is not capable of attaching to the wall itself - worried about that becoming a problem. What are my options?

Even if you don't use a climbing vine, perhaps a plant liking low light wouldn't crawl toward that western light. Just seems all wrong and backwards for plants- they love east light and south exposures, North is cold and west is late afternoon sun. Did you have any idea what you wanted before you hung the lattice? Do you plan on incorporating plant lights for the plant/s? Where are you located to give us an idea of plants in your growing zone? Even if it is in an apartment or home, temperatures in your home can affect your plant/s.

Considering the light available, you would be looking for things like Pothos, small Monsteras and vining Philodendrons. There probably isn't enough light for anything with flowers.
Interesting project, hope you do something fun with it.