The Lone Wanderer Perk's current description at rank 1 is -
"Who needs friends, anyway? When adventuring without a companion, you take 15% less damage and carry weight increases by 50."
With the companion Dogmeat in your party you will still get the Lone Wanderer bonus. I know Dogmeat is a companion but is this a glitch or an intended game mechanic aka do they have plans of potentially patching it?
I would like to see some kind of official confirmation because everyone right now is speculating that it's a bug. Personally I think it was intended because "Lone Wanderer" is always pictured with his Dog in trailers and pictures in the original Fallout 3 and it's the same in Fallout 4's "Wanderer" trailer.
EDIT: Asked support. I'll post their answer if they get back to me soon.