Mycroft Holmes doesn't do sentiment. He's too busy running the British government, not to mention keeping a weather eye on his wayward sibling; love is just an unnecessary complication, one that's simply not worth his time.
Casual sex is more to the point, though he always makes sure it comes without strings attached. That's until he ends up in bed with the wrong bloke, and everything falls apart.
Greg Lestrade is a good man. Solid, down-to-earth, dependable. One of the very few people who understand how Sherlock's shenanigans deeply affect his big brother.
He finds himself yearning to let the other man in, but that's an option Mycroft simply cannot afford. Mixing up business and emotions isn't advisable for someone in his position, so he settles for keeping the Detective Inspector at arm's length and ignoring whatever happened between the two of them.
Lestrade isn't exactly happy about the outcome, but he shrugs it off eventually; his failed marriage has probably taught him as much. Their working relationship falls back into strictly professional, the tentative friendship they've been building up for so long completely forgotten.
There are nights when Mycroft sits alone nursing a glass of Scotch, walls closing in on him like a prison of his own making. He's not lonely, he murmurs in the quiet of his empty house; loneliness is for ordinary people, while he's far from ordinary himself.
It doesn't take long for Sherlock to notice; his little brother being his usual annoying self provides a somewhat welcome distraction, and yet he finds that searching gaze surprisingly unnerving for some reason. He fully expects the brat to call him on that, but at least he's spared the unpleasantness of it. It's a small mercy, and one he's actually grateful for.
Later on he realizes he's been slipping, when he's faced with a frustrated Scotland Yard Inspector that has just barged into his sanctuary at the Diogenes Club.
"Holmes, we have to talk," that's all Greg says, and something warm stirs inside Mycroft's chest.
(Something that feels suspiciously like hope, though he doesn't dare to acknowledge it yet.)