Antonyms for the phrase "threw lot with" could vary depending on the context in which it is used. However, generally speaking, antonyms for this phrase could include words or phrases like "abstain from," "disassociate with," "remain independent," "stay uncommitted," or "separate oneself from." Essentially, antonyms for "threw lot with" express the opposite action or behavior, where an individual chooses to distance themselves from a particular group or cause, rather than aligning with and supporting it. This could be the case in situations where one disagrees with the group's values or actions, or simply chooses to remain neutral or uninvolved in a given situation.