From the 777/787 FCTM Sec 4:
"The FMC provides maximum angle climb speeds. Maximum angle climb speed is normally used for obstacle clearance, minimum crossing altitude or to reach a specified altitude in a minimum distance. It varies with gross weight and provides approximately the same climb gradient as flaps up maneuver speed."
So, because on a jet, Vx is very close to V L/Dmax, your memory of 'the best lift to drag speed for the B777 is the flaps up manoeuvring speed' is close enough.