If you arrived at a Z gate from IAD (since the new pier A+ opened in October) you shouldn't have needed to clear security (passport control only) before your connecting flight to LYS. If you had arrived in B or C it's a different matter.

Where did your LYS flight depart from? There was no need to travel on the train if you arrived in Z and departed to LYS (presumably from an A gate). No wonder it took 45 minutes from gate to gate if you took the scenic route by train.

Since the OP is connecting from Schengen to non-Schengen, there's no need for security check in FRA unless the flight to IAD departs from a C gate.