Mr. Collins knew Lydia behavior. He saw it personally in Longbourn and Meryton, like when she interrupted him when he was reading, and perhaps in the Netherfield ball or at Mr. Phillips' home.

Charlotte could have said something that Elizabeth told her some time, that her parents indulged her younger sisters very much.

I suppose that Elizabeth must have written to Charlotte after she came back to Longbourn, and mentioned that Lydia was going to Brighton, and that she was worried for Lydia's behavior.

Why Mr. Collins had to tell Lady Catherine about the elopement?
Perhaps he thought that she was going to do something about it?
I have an image of Lady Catherine chasing Lydia and Wickham, and scolding them into harmony and plenty. ;-)

Then he says:

And this consideration leads me moreover to reflect, with augmented satisfaction, on a certain event of last November; for had it been otherwise, I must have been involved in all your sorrow and disgrace. (Ch. 48)