Eloise, sure we can do that, eat after the Lion King, if you like, it would be fun and is sort of right across the street. That is if you don't mind eating late. The show is 2 hours and 40 minutes long with a 15 minute intermission, so that puts us at 9 pm eating, if it suits you it suits me.
Maybe we have time before hand if we can get near the glass, to have a coke and look down on Times Square in the daylight too in their other lounge.. There are no reservations unless you want to eat upstairs (very pricey) and long lines. Alternatively they open at 4:30 but that's eating in daylight.
Speaking of Times Square there are two exciting happenings while we're there. They are filiming the new Arthur with Helen Mirren all over the city so you MAY stumble on a film crew and the stars while out walking.
In addition there is another "Happening" in NYC on the 12th, our Ellis Island Day, Sunday at 11:30 am in Times Square hosted by Kelsey Grammar, who is on Broadway, it's live free performances from The Addams Family, American Idiot, Billy Elliott, Chicago, Elf, Fela, In the Heights, La Cage aux Folles, The Lion King, Mamma Mia, Memphis, Million Dollar Quartet, Priscilla Queen of the Desert, The Phantom of the Opera, Promises Promises, Rain, Rock of Ages, The Scottsboro Boys, West Side Story and more... This all free on Times Square...expect crowds and roped off streets.
So if you don't plan to attend a Broadway show, Broadway will come to you free during that time.