I guess they never adjusted their thinking, but once they knew where the meeting would be the Corleones maybe should have discussed sending a dozen guys through the front door together instead of having Michael grope around for that little gun.

The driver doesn't have a name in the novel, and the restaurant is called "Luna Azure." In the movie, the former is given the name Lou and the latter is changed to Louis Italian-American Restaurant. It seems very unusual to introduce unrelated people named Lou and Louis in consecutive scenes. It appears likely, then, that Lou and Louis are the same person and that at the moment of the shootings he was in the kitchen prepping his cutlets for the next day's lunch crowd.