One's "destiny laying in" something is a common specific phrase. While less poetic, the meaning is essentially: "My destiny is to..."
"Implement" is not a good synonym here. To implement something is to start or to initiate it; to bring something into being.
The connotation of "to fulfill" can be understood by reversing the parts of the word: it is "to fill (something) full", or said another way, to complete, accomplish, or provide what is necessary for something to receive everything it needs. One can fulfill one's destiny, or fulfill one's potential, for example.