Homelander does die in the Boys comic. It happens due to a combination of factors including his own actions and the opposition he faces from other characters.
In the Boys comics, Homelander's story takes many twists and turns. He battles with his own inner demons and external enemies, and his fate is quite complex and unpredictable.
Homelander dies in the Boys comic when he's finally overpowered by a coalition of characters who've been working against him. It's a dramatic and conclusive end to his tyranny.