]On their first day at Rosings they can't be tired of Lady Catherine yet. The news of Mr Collins that Lizzie was staying with them must have had such attraction that they decided to go there at once.

I agree that it was because of Lizzy, but Col. Fitzwilliam had visited his aunt enough times to know what kind of visit he could expect there, which IMO is why JA writes that he needed some relief. I think he was anxious to make a new acquaintance in Lizzy, in the hopes of it making his entire visit at Rosings more bearable.