Which class were you in? Economy? If you were then the limits for flights from the US on United are clear at ONE piece of baggage up to 23kg. Since you have "Premier" your allowance is 2 pieces of baggage but still 23kg.
However, you flew Lufthansa. Their limits for Economy are ONE case at 23kg but NOTHING extra for being a "Premier/Star Alliance Silver",
Lufthansa baggage .
So they were within their rights to charge you for the extra bag, whereas if you had flown United you would have been ok IF your baggage did not exceed 23kg.