I am going to be giving a presentation on colonial lanterns at this year's Tinsmithing Covergence, to be held at Sauder Village Ohio.
While doing some research for the talk I noticed that nearly all of the lanterns depicted in the etchings and paintings from the 18th century that I came across, were round. There are numerous existing lanterns attributed to the 18th century, but it looks like, from this very un-statistical study, that round was the way to go.
In talking with other tinsmiths about this it was pointed out that it is easier to make a round lantern with the tools used in the 18th century than to make a square lantern. So maybe that is all there is to it.
Here is an example from Hogarth: