Now if you were talking about just bitter (singular), I could safely say you were in luck, because you could walk into any pub in England and order a shandy (which I rather enjoy, despite being a Yank, but of course I love bitter as well... and lager, and stout, and porter, and pale ales, and heifewessen, and so on and so forth.)

But as for a lemon-lime and bitterS, nope, I don't know that I've ever heard of such a thing until now.