Part of what enables me to trust him is that I see him telling the truth everywhere. If he was still lying, I would be very concerned about another A. I doubt we would be in R.
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.
All cheaters are liars. Not all liars are cheaters. Are liars more prone to cheat? I don't know; I suspect that those who do not value truth and integrity do find it easier to slide down that slippery slope, to conceal their behaviors, to lie and hide and harbor secrets.
And for the subset of liars who cheat--then yes. ABSOLUTELY, there is a connection between the two behaviors. Until and unless the tendency toward dishonesty is addressed and corrected---replaced with different and more adaptive behaviors---then the risk of heading down the infidelity rabbit hole remains very real.