If it’s all on one itinerary and you have a same day international segment, you should be fine.
As Star Alliance Gold, the rule is access when traveling on a same day international itinerary. It doesn’t matter that your first leg is domestic. What matters is that you’re connecting to an international flight and can show that boarding pass.
I’ve done this before at the origin airport with a domestic first leg and had no issues. Just showed both boarding passes in the app.
Sometimes phone agents mix up United Club rules with Star Alliance Gold rules, which aren’t the same. The lounge staff usually go by what’s in the system when they scan you.
As long as it’s same day and on a Star Alliance carrier, you should be good. Worst case, have both segments pulled up and point to the international leg.
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