There are several synonyms that can replace the phrase "had a lot to do with". Some of these options are "influenced", "affected", "contributed to", "played a role in", "was instrumental in", "was a factor in", and "had a hand in". Each of these phrases conveys the idea of being involved in a significant way or having an impact on something. They can be used interchangeably with "had a lot to do with" in a variety of contexts, such as discussing the causes of an event or the reasons behind a decision. By using synonyms, one can add variety to their writing and communicate their ideas more creatively.