Yes.Exterior wall of the same building that has the service supplying the panel ?
If the subpanel is on the same building as the electrical service (main panel) no ground rod is required. If a separate building, then you need a rod.Installing a 125a subpanel on an exterior wall to serve pool equipment. Should I drive a ground rod, in addition to the equipotential grid, for lightning protection, since the panel will be mounted on an exterior wall?
Not required but you can certainly install one and connect it to the EGC bus in the sub-panel.I was wondering more about lightning protection, rather than equipotential bonding, since the panel is on the exterior of the house, but not near the service entrance.