I thought OP said she didn't go into his space (the bedroom) The bathroom is off a shared hallway - I think hat does make a huge difference.
I'm not sure how they work elsewhere, but here (England) ,most bathroom fans are already on a timer, the thing is, the timer is triggered by the light being turned off, so the timer wouldn't kick in if the lodger leaves the bathroom light on. I'm not sure whether it is the same in Ireland but here there are planning regulations which apply to ventilation for bathrooms and I strongly suspect that a timer which potentially turned off the fan when someone was in the bathroom (i.e. after a set time, regardless of whether the light was on or not) would not comply with the regs. So just putting a timer on may not be an option.
It also seems to me that installing a timer rather than having a conversation about making sure lights etc are turned off is overkill. Expecting someone to turn the bathroom fan / light off when the room isn't in use is not interfering in their space, it's a perfectly normal expectation of anyone living in a house.
Margo is correct about the location of the bathroom (smallish, shared hallway that I have to pass through on my way up or downstairs) and the fan timer being linked to the light switch. The funny thing was neither nor anyone else in the house had ever noticed the fan much before (though I guess anyone previous might just have been the sort to switch off lights automatically), but I had a temporary guest staying a while back, and he drew it to my and The Lodger's attention that the fan was noisy and we should turn it off! Since then I have been aware of it, and it IS kind of noisy, and while it obviously doesn't bother The Lodger as he's the one who leaves it on, he works long shifts and comes home very tired, so I've been sort of concerned he might fall asleep ok but it might wake him up later on. That's not an excuse and it has been illuminating reading the posts of those who think I did over-step. I do need to take that on board as the reason I am so concerned is that I do try to be a respectful landlord and I would hate for him to feel uncomfortable (which I am sure he does now).
I would never enter his bedroom. I've gone into his bathroom once or twice relating to maintenance issues but I don't frequent it. However I do switch out the light/fan probably pretty much nightly and I think I am getting too fussy about it - it overrode my default setting to stay out of his space.
If it makes a difference, we usually tend to keep very different hours so I am the last one in bed by several hours, so I usually make a last round of the house from my own point of view - switching off the internet and heating if it is on etc.
In all honesty I think it was just a case that neither of us expected the other one to be around and I feel we were both wrong. I wouldn't mind too much catching him walking around in his underwear for example, or brushing his teeth with the bathroom door open, I do think in a shared house he should be respectful of me as well as I of him!
He's quite reserved so while I would like to apologise, I also don't want to make him more uncomfortable. But I think it might be the right thing to do based on all the responses...