dessert and coffee near lyric opera house??
Before the opera, try the Maxim's joint on Madison located three or four blocks east of the Opera House. It's not high-luxe or expensive, but the desserts are really very nice, the coffee's okay (cappucino's better), and it's clean and quiet. Haven't been there in a while...but I recall liking it for an omelet and a glass of wine before going over to hear the fat (or skinny) people sing.
After the opera, I have had good luck at the Italian Village...particularly at the ritzy main-floor dining room, if I had the scratch to spare.