Upvote:5
With Lufthansa you can always bring a carry on and a personal item, as mentioned on the page https://www.lufthansa.com/de/en/carry-on-baggage. The problem is, that the part about the personal item on that page is not translated to english. It's the part under "Zusätzliche kostenfreie Gepäckstücke in der Kabine", which says
Ein weiteres kleines Gepäckstück (max. x=30 cm y=40 cm z=10 cm, z. B. Handtasche, Laptoptasche).
Translated by me:
Additional free items in the cabin: One further small luggage item, max 40x30x10 cm, e.g. purse, laptop bag etc.