Just allow to keep PIP window above screen lock window. This should be optional. Allow also to hide this window, while screen lock active.
Some times I go to kitchen and look from there on my PC monitor. This is quite useful, but for better security, why do not allow to lock session. I must say, I do not look at my PC every time I am at kitchen, but take a look for a while - on most interesting moments, I will say. When I have quests, go to kitchen to prepare dishes, I do not know If some guest would not use my computer.