I am looking for a fun/lively restaurant in the Gran Via, Puerto Del Sol area in Madrid for a group of around 15 people. Themed restaurants, Mexican, Italian, Spanish food is fine. Thanks.

The wife and I just got back from Madrid 2 weeks ago. We had a nice dinner at Asador de Aranda in the Sol area. They start seating people for dinner promptly at 9 pm. We arrived early and diners were milling aound their bar sipping cocktails and having tapas.
The main feature of the restaurant is their roasted lamb dish. The roasted leg of lamb that we had was well-cooked, very juicy, tasty and including the crackling skin and without the gamey taste. According to their website, they only serve special "baby milk lambs" that are bred in certain area of pain.
We went on a Friday night without reservation and the place filled up very quickly. I assume that for a large group, reservation is a must.

I don't believe you'll find any (many) Mexican restaurants in Madrid. Stick with the very fine Spanish food available and you won't go wrong.

paulinbermuda,
Any of the roasting taverns, the "asadores", in Old Madrid would be lively and fun, provided that you like roasts/red meats, that is, although some, like Posada de la Villa also serve really great fish dishes as well.
The Asador de Aranda would be the most convenient to a Gran Via hotel.

Besides the "Asador de Aranda", and a bit further afield, there's the lengendary "Antigua Casa Sobrinos de Botin" on Calle Cuchilleros, below the Plaza Mayor (tons of opinions posted here about it-strolling "student" minstrels come in the p.m. to serendade, and lots of tourists), "Casa Paco" (well known for steaks) on Plaza Puerta Cerrada, before crossing over to the Cava Baja, then on the Cava Baja there's "Posada de la Villa", my favorite of the above taverns, attracting more of a local crowd and always lively. As you walk in, to your right you'll see their huge and ancient roasting oven. Tapas bar downstairs and dining room upstairs. Nice wine list. Very atmospheric, and Old Madrid coaching inn dating from the 1600s.
www.posadadelavilla.com (for a group larger than 10, you can't book on line, must call)
But all these spots are very popular, so as rcc says, for such a large group, I'd have your hotel book in advance, particularly for a weekend night.

Of course, in Madrid there are many Mexicans restaurants, one of them is 'El Cuchi', besides Plaza Mayor and Arco de Cuchilleros, MichelleNYC.

The question is, why are you crossing the ocean to eat in a Mexican restaurant?

I'm with Maribel, MichelleNYC & rcc suggesting Asadores and places like that, or perhaps a good tapas bar/restaurant where you can share several plates.