Lewis has lived and voted in California until recently, the GOP said.
Lewis said he owns two homes in New Jersey, including one in Medford that was purchased in 2005.
"Doesn't matter," GOP attorney Mark Sheridan says of Lewis's New Jersey addresses. "He's been voting in California. And under California law, that makes him a resident of California. He can't be a resident of New Jersey at the same time."
A response from Lewis's lawyers was expected later Monday.
The former track star said he transferred his voter registration last Monday, the same day he officially declared his candidacy as a Democrat in the state's 8th District.
The 49-year-old political novice grew up in Willingboro, N.J.
The GOP filed a complaint to New Jersey Secretary of State Kim Guadagno, asking that Lewis' name be pulled from the primary ballot.