From just a basic perspective, the more moving parts, the more things that can fail. It would make sense to me that a lever gun would be more prone to failure as it does have a lot going on.
FWIW, revolvers are considered to be pretty reliable. Their mechanisms are actually complex. But they are "mature". Oh, and the number of parts and complexity of a pump shotgun and a lever action rifle are about the same. They work on similar principles. Nobody really questions the reliability of pump shotguns. Both pump action shotguns and lever action rifles are now able to be considered "mature". OTOH, autoloaders have their own reliability issues, and in many cases have a high degree of complexity.
Parts count and complexity really aren't all that relevant regarding reliability. The maturity of the design is more important.