One strand is fine, that's why it's laceweight! Although you could double-strand it if you wanted to (but then why not just use a thicker wool?).
Just use needles that are big enough - as specified in the pattern, or a couple of sizes bigger than specified on the label. Do a narrow version, 3 or 4 repeats, to decide whether you like the laciness of the fabric with your needles. If it's too loose and holey, use smaller needles: if not holey enough, use bigger. Once you have got a fabric that you like, undo it (or keep the swatch) and start the shawl proper.