"Lydia will never be easy till she has exposed herself in some public place or other, and we can never expect her to do it with so little expense or inconvenience to her family as under the present circumstances."

At first Mr. Bennet's reasoning for letting Lydia go to Brighton seems to have much to do with his own laziness and finances. Then the real reason is revealed

We shall have no peace at Longbourn if Lydia does not go to Brighton.

Listening to Lydia (and Mrs. B) bewailing the loss of opportunity that Brighton provided for weeks, if not longer, would probably drive Mr. B mad. He does have hopes that the journey to Brighton will provide Lydia with an important life lesson.

At Brighton she will be of less importance even as a common flirt than she has been here. The officers will find women better worth their notice. Let us hope, therefore, that her being there may teach her her own insignificance. At any rate, she cannot grow many degrees worse, without authorizing us to lock her up for the rest of her life."

I think he forgets that Lydia is not really into life lessons.