Electrical – Is it OK to attach only the junction box ground wire, or is it necessary to also attach ground wire from lamp fixture

First recommendation; put labels on stuff. Sorry, nobody needs a Monday Morning Quarterback.

Do you have a meter? I would try metering out which wire gets voltage with the lightswitch going on and off.

My guess, based on the two way switch, is that the three black wires are; Line ( from the breaker ), feed to the outlet, and feed to the switch. The two whites in the wirenut would be the Neutral to the breaker box, and the outlet. I am guessing that the single white wire is a carrier from the switch, or in your case, switches. With this premise in mind I would check the voltage with a meter on the single white against ground while blinking the switch. If the meter blinks with the switch, then put the fixture black onto this wire, and white with the wirenuted whites.

If this guess is wrong, I have more questions. Did / does the outlet loose power when the lightswitch is off? If yes, then it's probably wired with all blacks together and all whites together. But again, I'd check with a meter before closing in all the boxes.

good luck, let us know the outcome

The instructions for the fixture are only correct for a metal box. If a metal box was used, the box itself would (should) be grounded. The bracket that holds the light would then be connected to the box, which would make the bracket grounded. Finally the ground wire from the fixture would attach to the bracket, grounding the fixture.

In the case of a plastic box, the box is not grounded. All ground connections must be made by connecting the ground wires together. So in your situation you are correct, you'll connect the ground from the supply to the ground from the fixture using a twist-on connector (or other approved connection).