By full, that means not being able to see the bottom of the river due to the amount of eels present.
We ate them all.
The eels made it all the way to the Sargasso Sea and back, for breeding purposes. Clearly they would not be able to get from the sea to a fully landlocked lake, with no route to the sea.
However, my point is that we had so much marine life before we cleared out the rivers, to then need the sea, to go from coastal waters to the depths of the Antarctic ocean in the quest for any fish that have survived previous quests. It is just hard for us to imagine the abundance there once was, and, therefore, the relative ease to populate an isolated alpine meadow lake with fish in former times.