There are several synonyms for the phrase "live on," depending on the context in which it is used. One synonym is "reside," which implies a more permanent type of living arrangement. Another synonym is "dwell," which can also imply a long-term living situation. "Inhabit" is another synonym, which often suggests a more natural or organic type of living environment. "Survive" can also be a synonym for "live on," often referring to someone who has overcome difficult circumstances. Finally, "persist" is a synonym that can mean to continue to live on despite obstacles or challenges.