When expressing the idea that something or someone is closely related to a particular situation or event, one can use a variety of synonyms for the phrase "haddest lot do with". These include "connected with", "involved in", "associated with", "engaged in", "participating in", "contributing to", "influential in", "fundamental to", and "essential for". Each of these phrases emphasizes the idea of a deep and meaningful connection between the subject and the activity or circumstance at hand. Whether writing or speaking, it is important to choose the most appropriate synonym to convey the intended meaning and impact of the message.