[The Might]

I think the reasons why the Ring-bearers (Frodo, Bilbo, and eventually Sam) are allowed to go to Valinor are made pretty clear in LOTR.

Still you are 100% correct, this is the reason why lembas was such a well guarded secret.

This food the Eldar alone knew how to make. It was made for the comfort of those who had need to go upon a long journey in the wild, or of the hurt whose life was in peril. Only these were permitted to use it. The Eldar did not give it to Men, save only a few whom they loved, if they were in great need. The Eldar first received it from the Valar in the days of the Great Journey. It was made of corn which Yavanna brought forth in her fields of Aman and she sent some to the Eldar by the hand of Oromë for their long march. The corn of which the Lembas was made had the strong life of Aman and it could impart it to those who had the need and the right to use it, it could be sown at any season save in frost and it needed only a little sunlight to grow. The Eldar grew it in guarded lands and sunlit glades, they gathered it, each one by hand and were not allowed to use any metal tools. From the corn to the wafer none were permitted to handle this grain, except those Elven-women who were called Yavannildi, the maidens of Yavanna, and the art of making Lembas which they learned from the Valar, was a secret among them.

This was done because the Eldar had been commanded to keep this gift as a secret for if Mortals eat often of this bread, they became weary of their mortality, desired to abide among the Elves and long for the fields of Aman to which they cannot come.

Even though Melian was a Maia of Vana and Este, I guess she had learned this recipe from Yavanna some time during her stay in Valinor.