Best way to find a stud or joint behind lathe is a strong neodymium magnet. One scavenged from an old hard drive works well as they have a strong pull at the edge, allowing you to be more precise in locating the nails

Make a pencil mark where ever it sticks in the area you want to mount something, and the stud/joist will be indicated by a straight row of marks while any painted over or broken off nail in the gaps will be an outlier.