It's possible that two separate tickets were issued. A United ticket SFO-FRA, and a separate LH ticket FRA-MIL. If that's the case, the UA agent would not know what your final destination was. But, they certainly should have asked "is Frankfurt your final destination?" If not, they would have to add manually the LH information to generate a baggage tag. The "new" UA/CO computer system does not always issue the connecting boarding passes. Sometimes it does, sometimes not. But, that would not affect the final destination of your baggage and you can easily obtain a boarding pass for your remaining flights at your departure gate.
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