Hi again all,
Thank you for all the posts. I intended to reply sooner but life's been a bit hectic :-) I have a bit of an update, but first to clarify a few questions.
The bathroom is his for sole use. If I have guests they use a different one. (That said, he DOES use other bathrooms in the house, but it is up to me to sort it out if I don't want him doing that.)
The bathroom is in the shared hall, but it is exclusively his to use.
I don't need to go into the bathroom to turn off the light - I only pushed the door because it WAS a brain freeze moment. I take on board that I had no real right to be in there.
Here's the update though. It happened again. This time it was mid evening, we had been sitting downstairs chatting (so he knew I was in the house and awake), and he went off to do something. I had no real idea where, I wasn't paying attention. It sudden occurred to me I had earlier on shut the door of the spare room (not his room), and hadn't seen one of the cats since, and it was possible I had shut her in (the door is normally shut all the time but occasionally the cats open it or I go in and one of them follows me - they like the bed in there!). I ran upstairs to check. The Lodger's bathroom door was ajar, and I went straight past without looking at it, and into the spare room. Right enough the cat was in the room, so there was a bit of commotion as she ran out, no doubt relieved, and I apologised to her quite loudly. As I turned around to go back down the hall, I glimpsed The Lodger sitting on the toilet again. The door was only open a crack, about the same as it was initially last time (before I pushed it), but enough for me to see him. The difference was this time, having been into the spare room, I was facing a different way, so it was impossible not to see him as I went past.
This time I just figured - his call. I am not going to be embarrassed if he apparently doesn't care enough to shut the door so soon after the first incident. I WILL try to avoid going anywhere near his bathroom if I have any idea he is in there, but I do need to access both the spare room and the airing cupboard which is directly across from the bathroom at times.
Also, I don't think he's being deliberately creepy or anything. I think maybe it is just a thing in his family that you don't really bother to shut doors.