I do not believe that there is a main character in Louise Erdrich's Love Medicine. Each chapter is about a different character. The stories and characters overlap, but this is not a novel as much as it is a collection of short stories, realistically and poetically shared with the reader.
Newsweek author, Gene Lyons says:
[Regarding] Louise Erdrich's novel Love Medicine...that no matter what the dust jacket says, it's not a novel. It's a book of short stories...
As this is the case, it is impossible to find a main character because the book is not written as a novel, with one overriding conflict, a steady plot and a resolution to the story. It is written as a series of short stories with characters from the same two families. The chronology is out of sync. For example, the first chapter takes place in 1981, but the next chapter takes place in 1934; the story in the second chapter is related to the characters and story in the first chapter, but with a totally different plot, new characters—though somehow tied to previous and future characters. The themes are often the same, showing how the experiences connect the different characters and generations together, but the book does not read as a novel in the format we are accustomed to.
It is not a traditional novel, so I don't see that Love Medicine has a main character.
I think the easy answer is that the main character is the reservation, much like the main character in The Godfather is the Mafia. With that said, look at the family tree and see who is at the center. Lipsha is the main character because he is the character who grows the most in the novel (and I do call it a novel and not a series of interlinking short stories). Isn't the term "main character" reserved for he/she who grows the most? Also, Lipsha is the son of Gerry (the most interesting and magical...from the Pillager family) and June (the catalyst of the novel). Each character is linked through June and it is her death that brings the family, and the memories, back together. The easy answer is that there is no main character, so stretch yourself and say Lipsha is the main character. If you are writing on this topic, this answer will create the most interesting discussion.