Where does the "Lyrical" part come from?
Like a lot of this stuff, its probably just english that sounds cool - also Nanoha does use it in her activation key (which is barely ever used).

As for where it originally came from, Nanoha itself is a spinoff from Triangle Heart, a VN series about the rest of the Takamachi family, who are badass bodyguards - you can see the original prototype here: https://www.youtube.com/watch?v=G_RBghAfiW8