It amazes me how often the lathe is needed. Though I always wanted a mill and a lathe, it wasn't until I was in my 70's that I finally got them and taught myself how to use them. Still learning.
A lathe is the only tool that can make parts to fix itself.
If you also have a mill. -Al
Actually a knee mill also amazes at how often it becomes useful. And it really goes hand in hand with a lathe.
Mine is an ancient Index Super 55 (photo). Also shown is the very first part I made on it: an end fitting for a 4" diameter sailboat boom. I had never operated a mill before, so this was a great challenge for this old man.