The phrase "had lot to do with" is a common expression that means to be closely related to or heavily involved in a situation or event. There are several synonyms that can be used to convey similar meanings, such as "played a significant role in," "was a major factor in," or "was instrumental in." Other phrases that could be used include "had a substantial impact on," "contributed greatly to," or "was deeply involved in." Each of these synonyms helps add more nuance and depth to the original phrase, depending on the tone and context of the situation.