I assume we will need to follow the baggage sizes for United, not Lutfhansa, is that correct? I'm not really sure what this means.
It's a Lufthansa flight. United and Lufthansa codeshare which means the LUfthansa flight will have both a LUfthansa and United flight number. (You can always tell a codeshare flight if the number begins with 5000 or above.) It's Lufthansa's rule on board.
If the flight is operated by Lufthansa then you will probably be required to follow Lufthansa's baggage requirements. It's not a bad idea to have those requirements in mind anyway if you're planning on flying within Europe. Most of the European carriers have nearly ridiculous limits on carry-ons.
Lutfhansa operates something called "two piece flight" (I forget exactally what it's called) on their long haul flights. If your flight originates in the U.S. or Canada and say your final destination is Berlin your flight would be for example: Los Angeles to Munich, change planes in Munich to Berlin. You may check TWO bags plus have a carry-on. If you wanted to fly from Los Angeles to Munich, stay a few days and then fly on to Berlin (two separate flights) you would only be allowed ONE checked bag on the Munich to Berlin flight. It's important to remember you can only check in two bags on long haul flights where you don't leave the airport for your connection and it must be on the same carrier. I believe United is going to institute a $50 fee for a second checked bag but I don't fly them so I could be wrong. Economy class travelers are restricted to one checked bag and one carry-on within the EU except as noted above.
It doesn't matter how many different airlines are on the ticket you bought. It doesn't matter if they have different weight and baggage restrictions for hold luggage. The baggage allowance is clearly stated on your ticket, either paper ticket or etix ( if etix it is printed clearly on your email confirmation ). This is a legally binding document. All the airlines covered on the ticket have to abide by the hold luggage allowance stated on the ticket. If the ticket was issued by airline A and the check-in staff of airline B query it the issue is not with yourself but with airline A. This applies with codeshare tickets, interline tickets or any other ticket you care to mention. If there are variations of luggage allowances they must be clearly stated on each coupon ( paper ticket ) or sector ( etix ).
All too often this comes up because check-in staff are unaware of the terms and conditions on tickets. It's bad for the airline business. Complain - you're within your rights.
United and Lufthansa are Star Alliance partners. Since you are in Granite Bay, you will go from SMF to LAX on United where you will pick up the Lufthansa flight to Frankfurt. If I'm correct on LAX, it's a great flight to Frankfurt. We've done this out of Elk Grove. (Or, they may fly you to some other city to pick up Lufthansa).
As for luggage, you will be bound by the Lufthansa rules once you check in at the Lufthansa counter. The luggage restrictions vary between 2nd class and Bus Class/1st Class. CLICK HERE for the fun rules on free baggage. For carry on, 2nd class is limited to 8kg and there is a size limit (LxHxW). It's two 8kg bags for business class and 1st class.