Holmes brothers are supernaturals/otherworld and loose power/magic if they consort with humans. To get back the power/magic they must eat the human they consort.
Lust/Attraction = hunger. The more they like or attracted to someone, the more they want to eat that someone. To keep from eating the human they are attracted to, the supernatural/otherworld Holmeses eat other people to satiate or diminish the hunger pains.

Sherlock ate Victor Trevor.sherlock regrets and resorts to drugs so he will not be hungry.

Holmes brothers are finding it more difficult to hide from Lestrade/John. Mycroft is fat from substituting other humans to his hunger for Lestrade. Sherlock controlled himself thru drugs. When sherlock met John, Sherlock asked Mycroft's help to find substitute food that's why he gained weight. John thinks its his good influence. Sherlock makes secret drugs so he can control his hunger for John. Lestrade is overseeing more missing persons cases.
Problems come when Holmeses discover someone else wants to eat Lestrade &John