Development

Lucy and Desi finished their vaudeville tour in early 1951, as Lucy could no longer do such vigorous physical comedy because she was pregnant with her first child.  Work began on a pilot for the show, written by Lucy's radio writers, Jess Oppenheimer, Bob Carroll Jr., and Madelyn Pugh (the latter two would continue to write for all nine seasons of "I Love Lucy" until 1960).  "My Favorite Husband" had it's last broadcasted show on March 31st, 1951, and the pilot for "The Lucille Ball and Desi Arnaz Show" was filmed in kinescope earlier in the month.  In the pilot, Lucy is costumed entirely in oversized robes and pajamas to conceal her advancing state of pregnancy (she gave birth to daughter Lucie Arnaz in July 1951), and at the last moment, the lead characters names were changed from "Lucy and Larry Lopez" to what we all know them as now, "Lucy and Ricky Ricardo". 
Although by this point other networks were showing interest in taking on the show, CBS agreed to produce it, and a leading cigarette company, Philip Morris, agreed to sponsor.  At this point, Lucy, Desi, and all three writers decided the show needed a catchier name.  At one brainstorming session, Desi was thinking out loud, saying something to the effect of, "She can't sing, she can't dance, but she doesn't give up!  I Love that Lucy!" and the title of the show was born.