I think this is definitely a local problem and not part of the PoCo network.
What really needs to be ascertained, is how the lights are wired in that place.
If them lighting circuits are all sharing a common feed, I would suspect a dodgy neutral (or phase) connection somewhere in the installation.
More than likely on one of the lighting circuit home-runs.
An ohm-meter and a long piece of wire would help speed the fault-finding process up.

Mike, you never mentioned if the receptacle circuits were affected by this intermittent voltage sag problem.
Were these checked at the same time?, as that would also give you some sort of indication as to where the fault could be.

Hope this is of some help.