I have been on MSC Lirica but it was a cruise in the Caribbean. And will be doing another Lirica cruise next year.
On our cruise while there were a number of Americans and Canadians the majority of passengers were European.
On the formal night almost everyone did dress accordingly. On the other nights it was dress all over the place. I never saw anyone being told they could not come in the dining room ( one man even came in one night in shorts and what looked to me a white under shirt - not even a tank top in appearance) But how others dressed did not detere (sp) from the cruise.
The crew were all very nice.
I know this is not the ship or cruise you will be one but maybe this will be a bit of help for you.
Star Princess 2005, Sun Princess 2005
Caribbean Princess 2006, MSC Lirica 2006 , NCL Pearl 2007, Majesty of the Seas 2008, Carnival Destiny 2008, MSC Lirica 2009, Carnival Valor 2009,Carnival Legend 2010, Carnival Liberty 2010,Carnival Fantsay 2011,Carnival Valor Feb 2012, MSC Poesia Dec 2012, MSC Poesia April 2013, Carnival Legend Nov 2013, MSC DIVINA Jan 2014, MSC Divina Oct 2014, Carnival Liberty Jan 2015, MSC Divina Apr 2015, Carnival Ecstasy Oct 2015, NCL Star Jan 2016