I think our dear Lydia is being shown off as a member of the "boy of the week" club - I believe it was deliberate on JA's part to show how fleeting and fickle her attentions were, and to highlight the fact that while having someone to flirt/dance with was important, the particulars of who that someone might be were not. To me, JA did her own subtle version of saying "Lydia loved boys, she decided she loved boys in red coats best of all, and from that point on any boy in a red coat would do as well as any other."