Tyrtaios, the Attic poet, sent to Sparta by the Oracle to assist with the Second Messenian War, stated that the first war was fought by the grandfathers of the men who fought in the second war. That would put the timeframe of the second war at about 690 B.C. Technically his words were “the fathers of our fathers”, which could have been an imprecise use of the term, so the second war may have taken place in the middle of the seventh century.
The second war was not one of conquest but the putting down of a revolt. Toynbee suggests that it was the time of establishment of the Lycurgian reforms, not earlier as others have suggested. His reasoning was that the Spartan commoners would have demanded rights in return for their help in protecting the new kingdom.