Unless your Gallery app has a "lock" setting of its own (as above) there's no way of locking the Gallery app with a fingerprint without using a third party app (not sure why the aversion to third party apps - there's nothing special about the ones the manufacturer installs themselves). So a few suggestions:
1) Use a third party app to lock the gallery (there are a number of them, I've never used one so can't make a recommendation.
2) Use a Gallery app that allows you to hide or lock folders (but beware of easily visible settings that allow you to unhide them). You may have to disable the stock gallery app to stop them using that instead ("hide" generally creates a .nomedia file, see below, so will work with all gallery apps, but other options may not).
3) Put those photos in a separate folder and stick a file called ".nomedia" in there - that will stop it showing up in the Gallery app (you'll still be able to find them with a file browser).
4) Don't lend the phone to the nosy so-and-so's.