Should a dual band open stub j pole like the one arrow makes be
grounded or not? Seems like someone told me no j polls should be
grounded according to their nec program. The website says it can be
grounded or not.
If it should not, then how do you protect from lightening?
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Earthing any antenna does not protect against a lightning strike.
The best way to protect equipment attached to any antenna is to disconnect
the feeder near the radio equipment , keeping the feeder metal connections
away from any other metal.

When I go away from home expecting 'static' activity and lightning ,I always
disconnect the antenna feeders and 'park' the connectors inside a plastic
box

However ,earthing an antenna does help preventing static charge build-up .
Hence following a feeder disconnect ,before reconnecting it to radio
equipment , I briefly 'touch' the feeder connection(s) to earth.
My double ZEPP or Doublet wire dipole with balanced ribbon feeder has 2 ea
composite 47 kOhms resistor at the matching unit (tuner if you wish)
connected to chassis/earth.

Frank GM0CSZ / KN6WH