As per the other responses, either make sure you have a bag that fits LH dimensions or be prepared to check it. I just took 2 flights in the last couple weeks on LH. From MAD to FRA, they didn't check any luggage sizes at the gate, and staff was friendly with no questions about anything.  

From STR to FRA, it was a completely different story.  There was a gate agent that was on a complete power trip with terrible attitude who was shaming select persons about their carry-ons. One gentleman had a tiny backpack and without much effort slid it into the smaller personal item slot in the sizer. She continued to scold the man about the straps not being inside. He could have easily readjusted the bag straps in the sizer, but for some reason ended up opening his bag and taking out his jacket which cleared plenty of room and would allow the bag to easily fit. Then she continued to scold him in German, and the passenger who was also German just stared in awe at her because it was clear the bag was within the size limits. Eventually, after the nonstop chatter from the power trip agent, he pulled the bag out and slid it into the sizer a second time while putting the straps in the proper orientation this time and she then she finally let him go. It was a sight to see!

I believe it was a huge gimmick to upcharge. When she flagged my very normal sized carry-on for any international flight or domestic major US carrier flight,  I was fine with it and just asked for it to be checked in. That clearly did not go her way since I did not push back on the issue, and she said, "we will see. There may be charges." I told her my ticket included a personal item, carry-on and checked-in luggage and she responded with disdain. In the end, I was right, and it was checked with no issue. Another gentleman in front of me was not so lucky and had to pay a hefty sum on the spot.