While both names are associated with the state of Florida (Lilly Pulitzer with Palm Beach and Joseph Pulitzer with the Pulitzer Prize awarded in New York City, which was established by his will), they are not connected in any way.
Lilly Pulitzer was born Lilly McKim in 1937, while Joseph Pulitzer was born in 1847 and died in 1911, making it impossible for them to be related.