In Jane Austen's day, society was still a lot stricter when it came to acting upon one's religion, especially with respect to holy matrimony and premarital sex. A woman who had intercourse with a man out of wedlock was considered a fallen woman. She would have been completely ostracized from society, unless there was still a family member willing to take care of her. In fact, Mr. Collins proposed that the Bennet family do just that in his letter of "consolation." After Lydia runs off with Wickham, Mr. Collins writes to the Bennet family, opening his letter with a line offering condolences, but then closing his the letter by advising Mr. Bennet to "throw off [his] unworthy child from [his] affection for ever, and leave her to reap the fruits of her own heinous offence" (Ch. 48). Hence, one potential consequence of Lydia's actions is being ostracized, not only by society, but by her family as well.
In addition, as Mr. Collins points out, another consequence of Lydia's actions is that dishonoring herself will bring further dishonor to her entire family. Now that Lydia has a fallen reputation, no one of high society or having any wealth will want to marry the other Bennet daughters.
An economic consequence that directly affects Lydia is that now she has forced herself to be married a man who is very extravagant with money. Even though Darcy paid Wickham's debts in order to bribe him to marry Lydia, it is most likely that Wickham will merely rack up more debts in the near future. Therefore, Lydia has forced herself into a marriage that will always leave her in poverty.