What were the real circumstances of Lydia's marriage arrangements that Mrs Gardiner revealed in her letter to Elizabeth?

Elizabeth receives two letters from Jane at the same time. The first is short and panicked, the second more composed, but they together deliver terrible news: Lydia has run off from Brighton and eloped with Wickham. Though the Forsters expected the couple to elope to Scotland (where minors could marry without parental permission), the family now worries that Wickham actually has no intention of marrying Lydia at all. Jane begs Elizabeth and the Gardiners to return home immediately, in part so Mr. Gardiner can help Mr. Bennet search for Lydia in London.