Ola' Bernardo.
The Lemania 5100 can be a tough one for some watchmakers, I've heard horror stories and also experienced one myself before finding safe havens here.
So make your due diligence: if you choose to go via a local watchmaker, do make sure to ask them if they've serviced it beforehand. And that they have access to parts, which are getting scarcer and scarcer.
Otherwise some names here can surely help, though they're mainly located in Europe or NA - all of them excellent.
Another option is TAG Heuer themselves, but be aware they'll most likely strip your watch of the vintage parts and substitute them with service ones - and that it'll be surely costly as most likely they're going to ship it back to Switzerland.
Hope this helps.
Tchau,
Fabrizio