score:3
Yes, you can take personal item in addition to the other carry on per https://www.lufthansa.com/us/en/Carry-on-baggage . I certainly have never seen an issue with that.
This may not apply to an "Economy Light" fare, in which case they may be more strict.
Please keep in mind that the carry on has an 8kg weight restriction which they tend to enforce. Most "regular" US sized roll-a-boards are heavier than that when packed full, so make sure you weigh before heading to the airport.
Upvote:2
Most travelers take a laptop (or similar) bag AND the carry-on baggage, just as the less restrictive page says:
https://www.lufthansa.com/de/en/Carry-on-baggage
Just make sure your carry-on weights less than 8kg to avoid any trouble with it.
If you keep any concerns, you may take a screenshot of the page, or even print it. I' am sure you will not have any issues with your laptop, but you will have a good point to discuss in case you're asked to pay.