Hi, I'm Heather, an attorney with 15 years experience and I'd be happy to assist with general information for educational purposes.
There really isn't such a thing as a "normal" rental arrangement, because lease and rental contracts vary wildly.
I can tell you that most rental contracts will state that you have to have the landlord's permission to do improvements or modifications. This could be considered such, and if your contract says that, you would need permission.
In addition, most rental contracts would not allow you to do something that goes against building code. If the lockset requires a key from inside the bedroom, it would be potentially limiting escaping the room in the case of a fire, if the key were misplaced. Therefore, most likely, in order to be building code compliant, the lockset would have to be able to be manipulated by hand from inside the bedroom.
This is a modification that I think most landlords would be fine with - - especially if you provided the landlord with a key.
For practical purposes however, your landlord probably won't know if you make the change, and it might not be violating your lease if you do it without permission. You'd just have to read your lease terms to determine that.
Let me know if I answered your question.