In the poem "The Eagle", does the line "And like a thunderbolt he falls" mean the eagle dies?

i wouldn't say that he dies, but that is certainly an interpretation- that it was meant to be ironic. 

the first thing i thought of was that the eagle searches for prey from up high in the sky, and when he spots his prey, he strikes. he strikes with the power of a thunderbolt

but a friend of mine thought of Zeus and his thunderbolt. "Close to the sun..." so the eagle is high up in the sky as Zeus lives on Mount Olympus in the sky

still, the story of icarus draws the most similarities