The name of the exclusive restaurant in the film is "Il Mare". "Il Mare" is also the name of the house and the International title of the Korean film upon which "The Lake House" is based, Siworae (2000).
The actual house did not exist, and was built for the movie, then dismantled. In using Google Earth to see the house, enter 41.7142, -87.8901 in the window on the Fly To tab. This will take you to the center of the lake. Zoom to the clearing on the eastern shore. Then select April 29, 2005, as the date.
Sandra Bullock states that she felt compelled to name the dog "Jack" after the character of Keanu Reeves in Speed (1994) - the first movie the two of them made together.
The lake house measured two thousand square feet, and sat on top of steel beams ten feet above the waterline. It used 35 tons of steel, and required nearly one hundred carpenters, welders, and painters to build it.
Sandra Bullock revealed in an Entertainment Weekly interview that the title house had running water, but no toilets.