I mean, normally you'd expect the player to open the door of a cell first -by whatever means- and then check the containers inside the cell, that is the procedure most "normal" people would follow, as it is realistic. Otherwise you'd be either curious enough or randomly decide to check what is inside the accessible containers in the cell before you unlock the door. Even if Bethesda wanted to place the key to the door somewhere for the dumb and/or uninterested players, placing it into a container inside the cell kind of defeats that purpose. Not to mention would annoy everyone else who found the key in a container after struggling to open the lock.
The cell has a hidden stone door which opens by a lever I believe, then you go down following some stairs, the top part of the cell isn't a trap door, doesn't open. It is just there so that you can see the lizard below. The annoying thing is that the lizard sometimes stands too far away so you can't even initiate dialogue without going inside the cell.