Per the title, Bob Hope is an English born American icon that was successful in vaudeville, radio, movies and television and is well remembered for entertaining American soldiers in wars from 1941 to 1988.
In the 1950s, a part-owner of the Cleveland Indians baseball team, Bob Hope did a guest appearance in I Love Lucy (1951) centered around his attending a Yankees-Indians game at Yankee Stadium.
In the scene at the ballpark, when a boy asks for Bob Hope's autograph, Hope asks him if he's seen his new movie The Iron Petticoat (1956). He says Yes, sir! The show aired on Monday, October 1st, 1956 but the movie wasn't released in the U.S. until Monday, January 7th, 1957. 14 weeks & 98 days differ among these two dates.
In the scene in the Indian's locker room, Lucy is wearing #19, which was the uniform number of Bob Feller.