Some scholars believe Lycurgus lived in the early 8th century B.C. (circa 770), and others place him a century later. I believe the reforms were probably implemented after the Second Messenian War in 640 B.C. The Spartans had originally subjugated the Messenians in 708, but they revolted in 640, and had to be defeated and controlled a second time. Most likely changes were made then to prevent further revolts.
The earlier date seems unlikely, because writing was not established in Greece until 750 B.C, and it’s hard to imagine a Lycurgian Constitution before that time. Moreover, the first Athenian Constitution dated from 594, so putting the Spartans one hundred and fifty years ahead of the rest of Greece in the creation of a modern government seems farfetched.