Fellow working and nursing/pumping mom weighing in;
I'm really mad on your behalf. What a rude woman!!!
With a lock on the door, it makes it impossible to pump if this lady is in there, right? I would go to HR, explain that you need a room that is AVAILABLE to you for pumping on your lunch hour. Having the room occupied all the time is not the same thing. Ask if there is an unused office or
something. They may not be able to stop the woman from using the room for eating her meal, but they must be able to provide you with a private space for pumping. If it were another nursing mom, I'm sure they would ask you two to work things out between yourselves. But it's not a lunch room, and she doesn't need to lock herself away to eat a sandwich.
Alternatively, see if you can have them at least take the lock off the door and just muscle your way in every day. I have a cover-up that I keep handy in case someone walks in on me. (I pump in a "sick room" and there is no lock.) I know you don't want to be showing her everything.
In the meantime, go ahead and knock away!