I went back to the early chapters to see if there's any mention of it, and there's nothing. I mean Ted Sandyman makes sense to me. There's interactions with him in a pub, and he comes off as a very dislikable, trolling hobbit. So, it's no surprise when he gets mentioned again (I believe when Sam looks into the mirror of Galadriel) as Ted being up to some rotten mischief. But there's nothing prior on Lotho or Rose.
Well, there is a mention of Lotho, but that's more of just being Lobelia and Otho's son, and there is backstory on their feud with Bilbo. But it seems rather...intense just to accuse Lotho of all the evil-doing simply because of his parents.
'And something's wrong with the Southfarthing evidently,' said Merry. 'There's a shortage of pipe-weed.'
'Whatever it is,' said Pippin, "Lotho will be at the bottom of it: you can be sure of that." (Return of the King: Homeward Bound)
Pippin seems completely convinced whatever's going on in the Shire, it's that rascal Lotho's fault. It strikes me as odd that Lotho's misdeeds seem to be treated as a known thing by the hobbits, like he was a rotten scoundrel and "it is known." Later, Pippin even calls him "Lotho Pimple" and Sam expresses the desire to "punch him in his pimply face." That actually makes it sound like they dislike him because he's physically unappealing and different (like Grima being a pale, black-haired creeper in a blonde-haired sporty/war Rohan culture).
After lunch, the Sackville-Bagginses, Lobelia and her sandy-haired son, Lotho, turned up, much to Frodo's annoyance. 'Ours at last!' said Lobelia, as she stepped inside. It was not polite; nor strictly true, for the sale of Bag End did not take effect until midnight. But Lobelia can perhaps be forgiven: she had been obliged to wait about seventy-seven years longer for Bag End than she once hoped, and she was now a hundred years old. Anyway, she had come to see that nothing she had paid for had been carried off; and she wanted the keys. It took a long while to satisfy her, as she had brought a complete inventory with her and went right through it. In the end she departed with Lotho and the spare key and the promise that the other key would be left at the Gamgees' in Bagshot Row. She snorted, and showed plainly that she thought the Gamgees capable of plundering the hole during the night. (Fellowship of the Ring: Three is Company)
Lobelia's snooty unpleasantness is made evident in the early chapters, but I wouldn't say there's anything evident about Lotho, unless we just assume it's a guilt by association...Lobelia's his mother, he probably shares her same opinions?
Anyway, I doubt there is a definitive "lore" answer to be found here, unless I've missed it elsewhere? But even if there isn't, I'm kind of interested to speculate, and hear others speculation about who is Lotho? Who is Rose? What could Lotho have done previously to make our hobbit heroes utterly convinced he was the villain at fault while they've been away? What interactions did Sam have previously to be sweet on Rose Cotton? And maybe for our writers here, it will serve as inspiration in their fanfiction.