Contrary to Bug #20118, the Lone Wanderer perk should not work when Dogmeat is an active companion.
The load screen for this perk explicitly states that "with the Lone Wanderer perk, you'll take less damage and be able to carry more equipment when you adventure without a companion or dog."
There is no empirical evidence that supports the case that a perk called <u>Lone</u> Wanderer should work when Dogmeat is an active companion.
Originally, and during development, the player could have had a humanoid companion and Dogmeat simultaneously, which is why Dogmeat was implemented separately from other companions.
Per FollowersScript.psc:
<pre class="_prettyXprint _lang-nocode">
;************** NOTE ABOUT COMPANION AND DOGMEAT FUNCTIONS ******************
;Originally there were two slots for companion types, you could have both Dogmeat and a single human companion.
;That is why there are two aliases and two seperate functions.
;Now we are only letting you have either dogmeat or a single human companions.
;Rather than risk breaking everything by trying to unifying everything into a single alias/function call
;I am going to just put hooks in SetCompanion and SetDogmeatCompanion to auto dismiss the other
</pre>
This, however, has no bearing on the fact that the Lone Wanderer should not work while Dogmeat is an active companion, and instead only points to a feature that was cut.
AFAIK, restoring cut content is not within the scope of the Unofficial Fallout 4 Patch.
That the implementation of the Lone Wanderer perk continues to work while Dogmeat is an active companion should be viewed as an oversight, not a suggestion of intent (which is a subjective interpretation), especially when we have a load screen message that explicitly tells us that the perk should not work with "a companion or dog" in tow.
Furthermore, Bug #20118 was fixed in error and should have been classified as Not a Bug.