The phrase "hath lot do with" is an idiomatic expression used to describe the degree of relevance or connection between two things. It means that something has a significant influence or impact on another thing. Synonyms for this phrase include "is closely related to," "is strongly linked to," "has a direct bearing on," "affects," "influences," or "is intertwined with." Using these synonyms can help to convey a clearer and more precise meaning and make your writing or speech more impactful. It is important to use the right synonym in the right context to avoid ambiguity and confusion.