I've seen cases both ways. If there is a little ridge or shelf around the compartment, chances are there was some kind of cover.
In fact, my earlier cases do seem to tend to have been more likely to have had a cover but this is only a small sample so I don't know.
I prefer lids because I like to use the cases without everything going everywhere. Very few cases still fit so well that this is true without a lid.
But, the typical English case I have seen intends the lid of the overall case to be the lid for each compartment as well. In these the dividing walls extend well up the case interior.
