The lids for midgets are tough to get, sometimes it seems harder than the jars since lots of people have midgets without lids. I think you may be able to get repro lids for them if you simply want A lid. The midget jars are all pretty early as far as I know so that makes lids eaven harder to find.
In general midget jars are relatively rare but like other jar types some are a lot more rare than others. Consult the Red Book for the best info.
When you go to sell a jar like that having the right lid makes a big difference in value.