The work has been owned by the same family for 130 years.
When it last sold at auction, in 2006, it set Hockney's record.
Animation cels from coveted anime series like Dragon Ball Z, Pokémon, and Sailor Moon will be featured.
Phillips succeeded in tapping a Chinese buyer base with the auction.
Paintings by Churchill have generated attention at auction in recent months.
Marcello Kwan will serve as head of modern and contemporary art, and Cindy Lim will serve as the auction house's head of sales.
While most lots sold, the prices they commanded lagged behind artist records.
The collection was thought to have been lost since the 1930s.
The painting appeared in a New York Times Magazine profile that minted the artist as a star.
It took three years to recover the long-forgotten works.