I don't really know what "work" means. Usually people like ground meat to not be completely lean because the fat adds flavor and moisture.
But if you personally don't mind lean meat, then, well, whatever you want. The most common lean ground meat I've seen is turkey, often 99% lean. Sometimes you can find chicken too. Lean ground beef is usually more like 95% or 90%, but you can see what you can find.
I'd also note that the recipe doesn't sound great as written. Cooking ground meat for 15 minutes sounds over the top, and overcooked lean meat is probably even worse. Lean meat can already be quite dry and tough, and overcooking makes that worse. You should really only cook it only until it's done. Similarly, already cooked and mashed potatoes don't really need extra cooking. It can break down starch and make them more gluey and less fluffy.