I agree with many of the previous posters, that this situation seems like a small one, ripe for a quick, sincere apology after which everyone can move on. Since this topic was posted a few days ago, I suspect it's already been dealt with! I don't know if this thought would be useful for OP or lodger, but I have known many people who have been embroiled in bathroom fan imbroglios with roommates, so, to that end:
I lived in a tiny apartment with a few other girls in college, and we all had various friends and boyfriends coming in and out of the space, and sometimes we would variously run the fan and water in order to cover any potential noises, as it seems your lodger may. However, the fan-running is ambiguous (is the room occupied? is it unoccupied but the fan is still needed? is the fan merely grinding along, eternally forgotten?) and can echo weirdly into other rooms, and tap- or shower-running is needlessly wasteful. The solution we came up with was buying cheapo $10 iPod speakers to go on the bathroom counter, to play softly (not to blare, of course; no louder than the sound of water in a faucet, which isn't an unreasonable level) during times we deemed necessary.
Several years later, I still always keep cheapo iPod speakers in my bathroom. Great for singing along in the shower? Brushing one's teeth to new and refreshing rhythms? Jazzing up morning skincare routine! And, yes, occasionally provider of much-desired ambient noise.