Just to be clear: When you upgrade from economy to Business on LX with LX ticket stock for purely intra-europe flights: The lugagge allowance stays as per your original ticket. That is clearly stated in the rules. So a light fare upgraded to Business remains withhout lugagge allowance (is not called light any more).

Is your new ticket an lx or a lh ticket? I always thought you could only upgrade LX tickets.

Lugagge allowances have constant issues in the LH/LX Systems.
I once added lugagge later on light fare with LX Was not possible online for some wired reason. Agent literally told me: Do ignore everything you see online - even your Boarding pass will say no lugagge. However it will work at the Airport.
So it was - lugagge allowance went crazy on my recorde (show two on the Outbound an Zero on the Inbound) Boarding pass said "no lugagge" - still they took it wouthout discussion at the Airport both ways...

My take: Go to the Airport and argue there - if they really want money. Agents ther are mor knowledgable. If they really make you pay: sort it out by writing a letter to Basel (their head office). They are usually quite fast in dealing withe these kind of issues.

Two pieces of advice with Swiss:
a) if you can try to avoid English (German and French gets you more knowledgable agents) - valid for both phone calls and written comms
b) write physical letters to Basel (no e-mail or webforms - these will primarily treated by some bots and you get the most hillarious answers - without any relevance to your case)