The normal meaning of 'doyasıya' has to do with eating, i.e. eating until you are full. 'Doymak' has the sense of fulfilling a need. Here the reference is to love.

A life that passes without love is a thing that hasn't been lived
(In other words - Life has no meaning without love)
How can you depart from this world
without first having loved for all you are worth?
(Göçmek is used here with the sense of 'migrating' from this world to the next.)