In Austen's time, young couples sometimes ran off to get married just across the border in Scotland by the blacksmith. (I'm uncertain but I don't think you had to give notice of intention to marry or have the Banns read out in church.) Family members frequently set off in hot pursuit to prevent the match. However, if the marriage occured quikly as a fait accompli, although it would cause a stir in the neighborhood, I think a scandel could be lived down. But in the case of Lydia and Wickham, not only did they not go to Gretna Green, they lived together for about 2 months in London. Alone this would totally ruin Lydia's reputation. Of course, the idea of elopement is dreadful to Lizzy and Jane personally because they know of Wickham's dishonourable charecter. Then we hear in Jane's second letter to Lizzy that Wickham never intended to marry Lydia but took her to London. I think this is what is considered so dreadful, there was no marriage not even elopement to Gretna Green. Yet Lydia continued living with Wickham in London. People of the times will put such loose behaviour down to lust and carelessness. On Wickham's part, taking advantage of a silly, foolish girl. This is probably only part of the answer and it's unclear if Lydia really believed she was going to Gretna Green.