the High Sparrow is basically a medieval pope at this point. All the power is in his hands. Casually dismissing Grandma Tyrell (fuck you and your food), and having dirt on all the top players, he could put the fear of the seven gods into Tommen and make him his puppet.
LF did tell grandma that he had a guy...could it be the high sparrow? at first I thought he was talking about Lancel. But he's a true convert who feels guilty and wants to atone for his sins. He doesn't need to be encouraged to snitch on Cersei.
The high sparrow makes more sense. Grandma was right, he's got an agenda just like everyone else. Could LF have bought him off? on some "I'll take the L on my brothel, but you gotta do something for me"