Hi John, I'm related through the Broughton side, however, I've come across this post several times and wondered if you ever made a connection between the other Lundy's on the 1860 census in Mobile, AL.
Interestingly, of the 5 Lundy's born in MS, 4 are the sons of Abraham Lundy (1783 SC) & Elizabeth Arnold (1800 MS).They are all born in MS & all reside in Mobile, AL - makes me wonder if William A Lundy is a brother or related somehow.Have you ever found what his middle name is? One of the Lundy brothers has a son he named William Arnold Lundy (younger than your William or course - just made me wonder if the "A" could stand for Arnold).
If you haven't looked into those Lundy's already, thought it was worth a shot to rule them out or make them a possibility.
Good Luck, I'll let you know if I run across anything in the future!