The Lufthansa Site states this restriction on personal item size 30X40X10 CM. I have looked to see if the restriction is based on total linear size? Meaning, if I have a bag that is 26X38X16 CM will that be okay for carrying on as my personal item.
Not according to the rules. However, if your item e.g. is a soft backpack or a laptop bag, in reality you will most likely not have any problems. The main rule for the personal item is, that you have to be able to put it under your front seat, which will definitely be the case with your item.