The phrase "hadst lot do with" indicates a strong association or involvement with something. Some synonyms for this phrase are "had a hand in," "played a role in," "contributed to," "participated in," "had influence on," and "was involved with." These expressions convey a sense of agency and responsibility in relation to a particular event or situation. They suggest that the person in question was not a passive bystander but an active participant who had an impact on the outcome. Using these synonyms can help to add nuance and depth to your writing, allowing you to convey more precisely the degree of involvement of different individuals or groups in a given scenario.