MacKenzie is a common surname within the Scottish Highlands. Genetically, there are well over 50 un-related paternities sharing the surname.
There does not appear to be sources for William Lyon MacKenzie's father or grandfather. Instead, it appears all that is known is the oral tradition that he likely learned from his mother.
So, I would caution against spending much time trying to establish a connection further back than his Grandfather Colin. While it's very likely that his Colin was part of the Clan, because he left Clan lands, it's unlikely that he had an clear connection to the more prominent MacKenzie paternities. There were probably many Colin MacKenzies too.