backpack personal item or carry on?

It's not complicated: Every airline has their own limits for what they accept for the different kinds of bags: checked, carry-on, and personal item. It doesn't matter what the objects are, or what you call them ("backpack", "steamer trunk", "wheeled duffel", "man purse", whatever -- nobody cares). What matters are dimensions, and weights. All the allowed dimensions and weights are described on each airline's website. You go to their website, you write down their limits. You look at (measure and weigh) your items. You compare those against the posted limits. That's all there is to it.

The only questions are: how strict will they be in enforcing the limits, and how lucky you feel.

You can usually rely on them enforcing the limits for checked bags quite strictly. How strictly they enforce limits for carry-ons and personal items varies quite a lot, so it's impossible to predict with any certainty. It depends on things like the mood of the gate staff, how busy the flight is, how lucky you get, etc.

If you're lucky, they'll let some things that exceed their limits slide (usually only by a bit, rarely by a lot). If you're not lucky, they will enforce every rule strictly. You get to decide how lucky you feel.

So nobody else can tell you what will happen with your bags. If you want certainty, keep your items within the limits, and you'll be fine. If you are OK with having to re-pack at the gate, have your item gate-checked, be charged extra, or be denied, you can roll the dice.

That 4 inches for the personal item is depth, not width. So 16h x 12w x 4 deep for Lufthansa. Your daypack can be reduced to 4” deep (or thick) if it is lightly packed with flat items. But it may be over 16” in height—-many are.

I had look around before I found a good daypack that was 16” instead of 18”. It is an Osprey Skimmer 22L, made for small people with short torsos like me.

Check your airline. Usually, Your carry-on bag for the overhead bin can be 20 - 21”x 14” x9.” Then, you can wear a backpack or a tote bag that fits underseat as a personal item. Frontier airline which is restrictive allows 18”x 14” x 8” or 32 liters as an underseat bag just to give you an idea. Bags that fit this category include RS Appenzell backpack, Patagonia lightweight tote pack, wandf 16” bag on Amazon.com. You can use packing cubes to help with compression of items and ease of packing. Don’t try to put a larger bag underseat. Won’t work. Underseat bags hold about 3 days worth of clothing.

I just looked up Lufthansa. Your underseat item can be 16” x 12” x 4.” The economy free bag has to weigh under 8 kg. That’s about 17.6 lb.s. So, you can carry on two pieces in economy - one for the overhead bin and one underseat item. You may wish to consider a backpack for the overhead bin and a tote pack for your underseat item.

The personal item calculates to about 12.5 liters. The medium sized LLBean zip top tote would work as long as you don’t stuff it tight. Same for the wandf 16” bag - be able to compress it. A packing cube with a strap would work. Watch the dimensions.

Most airlines would count the backpack suitcase and a 21" rolling bag as two carry on's. All airlines have a list of terms and conditions--not all of which are exactly easy to understand.

I have been having more luck with one carry on bag per person on the larger legacy airlines than the budget European airlines. Sometimes the budget carriers will hit you up for the $ to check a bag.

I've just been rolling on the one bag with the backpack bag on my back and not questioned recently. They tend to be caught off guard when my wife rolls to the door of the airplane on a battery powered folding mobility scooter that must be gate checked and returned to the plane's door at the other end.

If you have $$$ to spend, RedOxx at Red Oxx.com has the metro laptop briefcase. It is 17” x 3.5” x 11 inches. I know it’s one inch too long. But, the bag is soft sided and can be compressed. I don’t know how rigid Lufthansa is. I think a generic tote bag or purse would probably still be your best bet here. Ameribag has some nice features and can be used as your day bag while traveling.

For what it's worth, I just flew on United to Frankfurt with a carry-on suitcase and a backpack and had no issues (other than the fact that my legs were a bit crowed in standard Economy with the backpack under the seat in front of me).