Indeed, the idea that educated people in the middle ages thought the earth was flat is a myth. It was well known to have been round since well before Christ.
Many early maps represent a round earth with edges covered by a sea. It is quite possible that the earliest of these actually are meant to represent a flat earth, but that's 6th century BC.
Of course, a couple of hundred years later it was well known, at least amongst Greek philosophers, that the earth was round, and Eratosthenes calculated the earths circumference.
This didn't stop the use of maps that made the earth look like a disc, though. So called "T and O maps" was often drawn as philosophical representations of earth, throughout the middle ages. These may have helped fuel the idea that people in the middle ages thought the earth was flat, but that was not the case. These maps are just representations in principle of the earth, and should not be seen as actual maps. That also means that even the 6th century BC map above may represent a round earth.
There was attempts to make real maps fit the T and O perspective, but even so this should not be taken as a belief that the earth was flat.
They can be interpreted as representing a belief that Jerusalem was located at the "top" of the earth, and that we all lived on the "top half", something that made theological sense.
Now about the question who believed the earth was flat, the answer therefore is "not many", but of course they existed. However, the mentioned Lactantius is the one of the few who is explicit, and clearly says that a round earth makes no sense. The other two we know of are Severian of Gabala and Cosmas Indicopleustes. These two both use religious arguments and basically says the earth is flat because it makes theological sense.
John Chrysostom and Athanasius of Alexandria both expressed the idea that the earth floats on water, and this is sometimes seen as evidence that they believed in a flat world. However, these quotes are rather arguments for God as a creator, more than arguments for a flat earth, so that interpretation is somewhat more tentative.
But although some scholars seem to have argued for a flat earth from a theological standpoint, most christian scholars clearly thought the world was round.