Cut/paste from:

http://www.cbssports.com/mlb/eye-on-baseball/22503679/photo-of-the-day-when-frank-sinatra-met-lou-gehrig 

...that's Frank Sinatra, who would've been just 23 years old at the time of this photo, getting an autograph from a widely smiling Lou Gehrig. Pictured at right is, according to Jonathan Eig's excellent book Luckiest Man, is Dr. Paul O'Leary of the Mayo Clinic, the physician who helped diagnose Gehrig with amyotrophic lateral sclerosis (ALS).

Gehrig's last game was April 30 of that year, and since this photo was taken before the final game of the '39 World Series (a Yankees sweep of the Reds), this might in fact have been the last time that Gehrig wore a baseball uniform. He would, of course, die of ALS some 20 months after his meeting with Sinatra.

About one month after meeting Gehrig, Sinatra, while visiting Chicago, would be invited to join Tommy Dorsey's band. He would accept the offer, and from that point his career would soar.