I don't see this as a big issue. Generally, tires wear pretty slowly, so unless you get a tire blowout from a large piece of glass, you should have plenty of lead time to order new tires. How long does it take the LBS to get the tires in stock? I would hope no more than two weeks.
Tires vary significantly on how many miles you can get. Rear tires wear much faster than front. Generally I would expect to get no less than a couple thousand miles out of an average set of tires.
One strategy you might consider is to wait until you wear out your current rear tire. Then, place the order for the tires you want with your LBS. At the same time purchase a single cheap tire to use until your new tires arrive. Keep the cheap tire as a backup in case you damage a good tire.