Obviously elopement was not a crime; nor was living with a man out of wedlock though it was a sin and perhaps the "death warrant" that Lizzy thought it would be if Lydia was allowed to go to Brighton. It was not an arbitrary choice to choose Brighton as the site of Lydia's elopement. According to the following sources:

1. "In choosing Brighton as the setting for the scandalous elopement of Pride and Prejudice, Jane Austen selected an appropriate and believable venue. Seaside resorts, spas and the towns where regiments were quartered saw more than their share of elopements during her lifetime and Brighton can be ticked off on all three counts. The place had a raffish character even before the Prince of Wales went there…All such resorts were happy hunting grounds for matrimonial adventurers, seducers and rakes, and women such as Lydia Bennet were regarded as fair game." (Jane Austen and Crime/Fullerton)

2. "It is the tacit acknowledgements of the restraints imposed by neighborhood society that Jane Austen usually removes her fictional characters to London or Bath or seaside resorts whenever they are about to behave in an outrageous manner: it was in…Brighton that Lydia Bennet eloped with Wickham." (Jane Austen and the Clergy/Collins)

3. "Brighton was a risque place, full of sailors and militiamen who were looking for a 'good time' while off duty. [It] was the home of the prince regent's seaside home, The Prince's Royal Pavilion,…[and he] was known for his sexual escapades." (Jane Austen for Dummies/KlingelRay)

4. "That Austen sets Lydia's ruin in Brighton with the militia comments very particularly on a specific social situation of her time. Brighton was one of the favorite playgrounds of the Prince Regent, whose lack of propriety, decorum and moral behavior was legendary. Many of the militia were stationed at or near Brighton, in fact, because of the frequent presence of the Prince Regent and Mrs. Fitzherbert, his wife/mistress at their lodgings in Brighton…Thus the fact that Wickham elopes with Lydia from Brighton, intending to enjoy her favors without the benefit of marriage…would inevitably remind Austen's initial readers of what many perceived to be the accelerated moral decline of the leaders of Great Britain, as well as convey Mr. Bennet's ineffectiveness as a father." (Literature in Context Series, PP/Teachman)