From what I understand it is possible to keep a South American Lungfish in a tank that is shorter than the fish. Several fish sellers in Buenos Aires told me that they do. So I would say that you might be able to grow a SAL to 4' in a 55g but it would be very cruel. I used to keep a 3' SAL in a 130g and the fish easily needed all of the space when it was active. So I too agree with the above posts.
As all lungfish grows pretty fast until they reach 1.5 to 2.5ft during first 1 - 3 years period. Thereafter, the growth rate will be very very slow because they need to build up the mass to grow even bigger and needing a lot of foods.
To house a lungfish properly (in my opinion) is to be able to let them, at least, turn around easily. So the tank size should be a square tank such as 3ft x 3ft x 1.5ft (Tank height is not important). So this kind tank's size, it should able to house a lungfish for at least first 5 years before need to upgrade to biggest tank.
the aquarium i volunteer at houses a 3 foot marbled lung in a small tank. im not sure on the exact gallons tho. i feel real sorry for it, he cant even turn around.