How did throwing King Arthur’s sword back into the lake relate to Merlin’s prediction that one day he will return to rule Britain again?

The sword could only be carried by the true King, and only a great leader could take possession. In returning the sword to the lake, Arthur was putting it back into the hands of the Lady of the lake to protect it.

“Then the king called Girflet and said to him, ‘Go to that hill, where you will find a lake; and throw my sword into it, for I want it to disappear from this kingdom, so that it won't fall into evil hands.’”