you will only have 1 free bag maa-ord. check the lufthansa website.

if you are ticketed thru united (starts with 016), then the confirmation email at the bottom will explain to you precisely and without any ambiguity what your baggage allowance is for every leg. this can also be located on the ua website travel management section or whatever

https://www.united.com/CMS/en-US/tra...edBaggage.aspx

my understanding of msc is that it is for the longest trip on your first leg
i also believe that ua allows 2x free bags on intl iteneraries (i dunno i nevre check bags)
so maybe you are on to something here, that you're entitled 2 bags for the maa ord leg