If your flight leaves at 6:29, there is almost no way you will make it, even cutting out before the bows. Into the Woods runs a full 3 hours. You'd only have 80 minutes or so to get your luggage from bag check, hail a car or a cab (not an instantaneous process right as a show is getting out and everyone else wants a car too), drive the 30-40 minutes to LGA, wait in the security line (even precheck is usually 10+ minutes these days), walk to your gate, and board before the doors close. And that's if everything goes right (you can get a car pretty fast, there's no traffic, normal security line, etc.), and you're not checking a bag at the airport.
For some perspective, I live a shorter cab ride away from LGA and usually leave 2 and a half hours before my flight to allow for traffic, lines, etc. 2 hours would be okay if everything went smoothly.
Updated On: 5/9/22 at 01:10 PM