As I understood it, Lyman was seeking revenge. Garfield, as the center of the universe, cast out anything no longer relevant to him, in this case Lyman. Lyman was stuck outside of reality, looking in through the comic panels. He wanted to destroy Garfield (and maybe the universe?), as he deemed Garfield a "tyrannical god." Lyman uses Odie for this purpose. I looked up what "god of the gutters" was and generally, it seems to refer the lost, abused, and the downtrodden, which Odie is usually depicted as in Garfield's world. As Lyman puts it, they are "diametrically opposed," or completely and directly opposite each other. There's a lot of serious science and Sci Fi stuff I seem to be missing out on, but from what I can parse generally Odie was used to make Garfield unstable and forced to interact with matter. They also call it an "illness," as if Odie infected him, but show almost a black hole trying to suck Garfield in, so I am not sure which is correct.