The death of Homelander in the comics was the result of a carefully orchestrated plan by a coalition of his adversaries. Each played a crucial role in bringing him down.
In the comics, it's a complex situation. Different storylines might have different outcomes, but as of the common ones, no one has directly killed Homelander.
I'm not entirely sure as I haven't read the 'homelander graphic novel' specifically, but typically in such novels, there would be a protagonist who is likely to be the homelander himself. There might also be supporting characters like his allies or those who oppose him.