Did Laurens really duel Charles Lee?

Yes, in December 1778

In the musical: in "Ten Duel Commandments", Laurens duels General Charles Lee, with Hamilton as his second.

The real story: at the Battle of Monmouth (28 June 1778), Lee ordered a retreat and was rebuked by Washington. After his court-martial, Lee kept attacking Washington's reputation. Laurens challenged him, and on 23 December 1778 they met; Hamilton served as Laurens's second. Lee was slightly wounded.

Fact-check verdict: true, including Hamilton's role as second.

References

Account of a Duel between Major General Charles Lee and Lieutenant Colonel John Laurens, [24 December 1778] (Founders Online, National Archives)
https://founders.archives.gov/documents/Hamilton/01-01-02-0687