There are several synonyms for the phrase "haddest a lot do with," which means to have been closely involved or influential in a situation. Some possible alternatives include "played a major role in," "had significant influence over," "contributed greatly to," "was a key factor in," and "had a hand in." Each of these phrases effectively conveys the idea that someone or something was instrumental in shaping a particular outcome or decision. Depending on the context, one of these synonyms may be more appropriate than the others, but all convey a similar sense of importance and impact.