You’re reading it correctly. On intercontinental routes, Star Alliance Gold gets 1 free checked bag even on Economy Light with Lufthansa and SWISS. It’s a status benefit layered on top of the fare.
The key parts:
It applies on intercontinental segments.
It usually must be added at the airport counter (not online).
It’s tied to your status being correctly in the booking.
The confusion from chat agents happens a lot because Economy Light normally has zero bag included, and some reps don’t mentally apply the Star Gold override.
For your itinerary:
LHR–Europe short haul segments:
Star Gold should also give you an extra bag allowance there, but Europe short haul rules can be slightly different depending on fare and operating carrier. Still, Gold generally adds one extra piece.
What I’d do:
Make sure your United number is in the booking.
Screenshot the baggage policy pages you linked.
Bring your digital Gold card in the United app just in case.
At the airport, agents are usually used to this rule. The phone agent confirming it is a good sign.
You should be fine. Just plan to check it at the counter, not online.
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