There are several synonyms that can be used instead of "haddest lot to do with." Words such as "influenced," "affected," "contributed to," "played a role in," and "had an impact on," can all be used interchangeably, depending on the context of the sentence. For example, "Her decision to leave the company was influenced by her colleague's resignation." Or "The weather conditions affected the outcome of the game." "His public statement contributed to the success of the campaign." "The company's marketing strategy played a role in their increased sales." "The new regulations had an impact on the industry." Each of these synonyms conveys a similar message, showcasing the importance of a particular factor in a given situation.