We flew 14 trips on Lufthansa (6 full trips, two where Lufthansa was only half) from 2011 through 2019. We fly with Rick Steves convertible carry-ons only. From the US we fly out of Philadelphia and connect onward in Frankfurt (one trip was Newark and Dusseldorf), our returns were from Venice, Budapest, Copenhagen, and Amsterdam, all connecting in Frankfurt, and once connecting in Munich (via a non-Lufthansa start). All trips were economy.
The packs are on our backs, and we were never asked to put them in the sizer nor weigh them. From our home scale we knew we were right at the limit and could move something to our folded up and packed away daypack for a hand item if need be. This included a couple times even stopping by the Lufthansa check-in counter in Philadelphia because I thought our home-printed boarding passes were not clear enough and I wanted their hard copies, no questions asked as we stood there.
The closest we ever had to a hassle was a gate agent in Frankfurt for our connection to Dubrovnik -which IIRC was a code-share and not specifically Lufthansa - stopping my wife behind me because her pack, on a 5' 1" person, was clearly too big. I turned and suggested that we switch packs, since they were identical and mine was not questioned. Gate agent was dumbfounded and we simply kept on walking to our A320, on which the bags easily went into the overhead.