lime washing

Has it been varnished at all? If so you need to strip that off first, but with pine, its often just a case of serious scrubbing with hot soapy water if it is an old bare wood finish. You could lime the grain, but you'll have to varnish it afterwards or at least use a sealing wax of some sort, and I personally think a properly soap scrubbed table looks so much better, plus you can take out all your nagst on it by scrubbing it periodically (much nicer to do than scrubbing floors)