This is my opinion: Hope its not too long.
The question is what is the lock for? Is it for when they are inside the room? or when they leave the room/house?So no one can enter even Totty or Mommy? Some people no matter what age they are like things to be private, have things a certain way, nice and neat not moved around things borrowed and not returned etc.. especially teenagers I think. Let's say if you live in a house with a bunch of kids and some have a tendency to take with out asking etc.. Or if they say they want to study/homework and the 10 year old needs to nudge at that time.
Now if it is for something like that you need to know who your dealing with, you need to have some trust, if you live in a smaller apartment or in a house where there is no place for some one to hide for some privacy to rest, read a book, study, then some consideration needs to be given.
One example I know a family that had to buy a little case with a lock for one child because the other had a eating disorder and they couldn't keep any nosh, snack for the next day laying around, it was either the the lock or nothing at all and that's not fear.
But the healthy adults are able to get in and put in nosh and clean the box etc..
Now if it's for when they leave the house the question is how old they are? If they are children that depend on your care no matter how old they are you should have access to that room at all times. And not because you don't want to trust them, you tell them its because you do want to trust them, Totty and Mommy also share the same room and there is a difference between hiding things and not touching someones things with out permission. It's ok to lock a door, but not to let anyone in is not right.
Now, if its an adult child living in your house I thing it depends on the condition's and terms you have worked out. It depends on the situation and if you feel you need to have access to that room then discuss it respectfully with them. Everyone is entitled to respect and privacy.
By the way I knock before entering my Second Graders room as well, if the door is not open. You teach them respect by giving it.