My electrical inspector told me all wiring on 20 amp circuits must be 12 wire. Is this true for wiring to lights from that circuits?

Yes!

Yet, I wouldn't say "all" wiring has to be 12 wire if served from a 20A OCPD. But, this is another topic.

Yes, #12 AWG is rated at 20 amps. There are occasions where because of distance problems you would have have to step up in wire size to compensate for the distance.

However, most general lighting circuits are wired with #14 gauge and are protected by a 15 amp breaker. #14 AWG is rated for 15 amps.