Learn English – the meaning of “notice to quit at once” and “Lotty points”

Lord Beamys led the way with Mrs. Gervase, Mrs. Dixon followed with Sir Vivian Ponsonby, and the multitudes that followed cried, saying, “What a dear old man!”—“Isn’t it kind of him to come all this way?”—“What a sweet expression, isn’t it?”—“I think he’s an old love”—“One of the good old sort”—“Real English nobleman”—“Oh most correct, I assure you; if a girl gets into trouble, notice to quit at once”—“Always stands by the Church”—“Twenty livings in his gift”—“Voted for the Public Worship Regulation Act”—“Ten thousand acres strictly preserved.” The old lord was leering pleasantly and muttering to himself: “Some fine gals here. Like the looks of that filly with the pink hat. Ought to see more of her. She’d give Lotty points.”

It's from Arthur Machen's The Hill of Dreams

1. if a girl gets into trouble; notice to quit at once

Who is receiving the quit notice and what exactly is a quit notice in this context? Is Lord punishing and firing some girl if she gets herself into trouble? There is no explanation in the book, that is all there.

2. Lotty points: I think the Lord here likes the girl and is then saying something inappropriate. Lotty points? What is that? I couldn't find anything. Is it the lottery? Or is he making a joke about horse racing? Because he likened her to a filly.