How do you unlock the image layer in pixlr?

Answer 1

In Photoshop by default Background layer is locked. To unlock it double click on layer and confirm on OK button in New Layer dialog, You are not creating another layer (title of dialog can confuse) but converting Background layer to normal which can be moved around or in another document. Another way to lock and unlock layer is to click on padlock icon at top of LAYERS palette. When layer is locked with this function, padlock icon is highlighted, click on layer to select it then click padlock icon to unlock layer.

Answer 2

You double click on the lock sign.

For relocking layers, I am not sure.