There is a movement towards lighter Bisques, in which the thickness would come from items such as a cooked potato puréed in milk. There’s probably a valid argument to be made, though, that if you’re pushing the boat out and paying for Lobster, you don’t want anyone using mashed potato to replace your full-fat, expensive cream. I suppose the killjoy versions probably leave out the dash of bourbon, too.
If you don’t know how to make Lobster Bisque, it may surprise you that some of the better, higher-end recipes use Lobster shells instead of Lobster meat. The shells are crushed or puréed and incorporated into the soup.
The Elizabethans made Bisque as a soup with meat and poultry. In the 1700s, it came to be associated with seafood.
Fannie Farmer listed a recipe for Lobster Bisque back in 1918. (She had you boil the shells for flavour, but then discard them and use meat in the Bisque.)