How thick is the door? If it's not less than about 1-3/8" you could probably bore it for a modern passage latchset. Usually they require a 1" hole straight in from the side.

If it's less than that, you might be able to find a European spec latchset for it. My memory might be off, but I seem to recall that EU interior doors are often thinner than those in the US.

It'd be sort of a shame to do it, though.. Those old gate style latches are almost totally trouble-free. Unlike modern latchsets, they just don't wear out. Friends of ours have one on their first floor lav. It's probably 100+ years old and still works perfectly. I wouldn't have said it was excessively noisy, though maybe a bit more so than a modern latch.

I wouldn’t change it. Try putting a little wd40 on it.