Sea lettuce might be given to goldfish, but only in a small quantity; this is to avoid it going bad before it is eaten.
Sea lettuce is not toxic if fresh and it contains minerals and vitamins that are good for your fish. Fish that are herbivores or omnivores will eat it (herbivore = plant eating, omnivore = mixed diet plant and meat eating).
Sea lettuce lives in salt water and is not able to survive in fresh water (it can survive short fluctuations in salt level, but not in fresh water).
When sea lettuce breaks down it release hydrogen sulfide; this is very toxic and it will kill your fish.
A truck driver was killed by the hydrogen sulfide gas from his cargo of sea lettuce, several people and animals like horses have died after being poisoned by this gas; more details about this in the Wikipedia article.
It can be hard to identify the edible types of sea lettuce.