Although lemons are plentiful here I always keep a small zip-lock baggie with lemon and orange zest in the freezer. In the winter when the oranges are cheaper and much better quality I remove the zest, that way I always have some handy. The same goes for lemons. Nothing like being in the middle of a recipe and having to stop to run out for a lemon, LOL.

I see no reason why you couldn't squeeze the lemon and freeze the juice for later use. I have kept the zest for up to a year with no problems.