I believe that people who lie on a constant basis, especially about things that are not really that important in the grand scheme, are absolutely prone to cheat and to cheat again. This includes people, like my exwh, who are masters at lying by omission rather than making overt untrue statements.
Lying is a way to avoid conflict and to avoid having to engage in authentic conversations about thoughts and feelings. Cheating is a sign that someone is, among many other things, cowardly and conflict avoidant. It is an escape from what is staring you right in the face - much like telling a lie. There is no way they can't be related.
Either way, lying and cheating are both symptoms of fundamental character flaws. As we always say around here, cheaters are broken. Broken people suffer from fundamental character flaws that, if allowed to go unrecognized and unrepaired, will always resurface. It's just their nature. Unless they want to really see it, and do the tough and consistent work to try to change it, it's always going to be that way.