I want to make it so that if someone turns the switch on, the lights will not automatically turn off. You might say, "But there is an option literally called "Switch to disable turning off". The problem is that if I do that, it never turns off because the app itself is turning the switch on. I might just be missing something though...
What brand/model switch is this? It probably will depend upon how or if your switch reports physical vs other reporting. Also, does this switch have double tap capabilities?
Also, does this switch have double tap capabilities?
Yes, but that's to complicated. My wife doesn't like having to remember different number of taps for different things. Hitting on to turn the light on is natural and easy to remember.
I think that does the opposite of what I want. I want it to not turn off if turned on manually.
Once you have that in place, it should follow the state of the physical switch. You can use that virtual switch in the Motion Lighting rule as your "don't turn off if" switch.