Lilly, a high-profile attorney who has represented multiple celebrities in the past, says he was hired within the last week along with Maurice Kutner of Miami, who will file the suit Monday morning in Dade County (Fla.) Family Court.
The suit cites a "long period of infidelity on the part or Mr. Rodriguez, an all-star baseball player for the New York Yankees." It also claims "emotional abandonment."
While the suit does not name pop music star Madonna as a cause, Lilly says A-Rod's "relationship with Madonna was the final straw for Mrs. Rodriguez."
Madonna, who is currently married to film director Guy Ritchie, has denied any romantic involvement with Alex Rodriguez.
Cynthia Rodriguez is in Miami and not available for comment on the advice of her attorneys.