Well look, there's definitely a reason to worry that LSH is gone. The show does such a tryhard job of establishing Petyr's lifelong obsession over Cat that it seemed like they were definitely setting up zombie Catelyn eating his face for sure.
LSH was there to wrap up Littlefinger's arc---which is actually the whole arc of the westerosi side of the novels---since Littlefinger started the whole thing. Everything from Robert's Rebellion, the fall of the Targaryens, the war of the five kings, all of it--Littlefingher hatched it about sixteen years before the start of Game of Thrones. It's basically all revenge porn hatched by poor nerdy little Petyr after getting gutted from groin to collarbone for challenging the bronzed superman Brandon Stark, Heir to Winterfell, to a duel to the death for Catelyn's vag.
So Littlefinger's father was a bro of Lord Hoster Tully's when they were both scared little pussies fighting against the Free Cities. This is important because the Baelish clan were Braavosi immigrants who have only been westerosi nobles for a generation. They still used the stone titan of Braavos as their house seal. (That stone titan is considered to be the "great stone beast" in Dany's vision in the house of the undying, which is a big clue). After surviving the ninepenny war, Hoster Tully fostered young Petyr Baelish at Riverrun, where poor sickly little Petyr fell hopelessly in love with Catelyn. Petyr reminisces fondly about his time studying and working with the maester at riverrun, reading all the books and working with the ravens and spending his free time with the Tully girls.
Now Catelyn was betrothed to Brandon Stark, because feudalism. But Petyr was a well-read young prodigy who practically lived in the maester's library/rookery (he would grow up to turn the entire economy of the seven kingdoms into profitability in four years) and as far as he knew, brave young underdogs are supposed to get the girl if they were brave and valorous and stepped up to unbeatable odds. So yeah, Brandon Stark guts him and was about to kill him when Catelyn steps in and gigglingly tells Brandon to "nevermind the boy". So there's our brave little geek roping his spleen back in while Catelyn is purring at her stud to grab her some lemoncakes and forget about silly little Petyr.
What's a heartbroken, lost, nearly-disembowelled boy-genius to do? Well first he spends months sucking down the castle's supply of milk of the poppy in the maester's chambers.... this is where Lysa sneaks in and deflowers herself on him. He's there at the maester's chamber recuperating from the lesson he teaches later Sansa about how realistic all the tales of chivalry are (not at all) when a raven arrives. The raven has news about Lyanna Stark---beloved sister of the buck stallion who nearly killed him and is prolly diddling the center of his universe---hanging out with Rhaegar Targaryen, probably out of her own free will. He could give the message to the maester just as it arrived.... or he could avenge himself and all sickly young nerds in the most awesome way imaginable.
Cut to twenty years later and zombie cat eats his face.
