Technical note: A symbol IN a coat of arms is always within a field of a specific color that has a obvious edge or border. The field may be a shield or a roundel or a cartouche or a flag or a medieval surcoat (thus the phrase "coat of arms").
In this case the shield is divided into four quarters, and the second and third quarters are red, with three gold lions passant. Symbols within one or more of the quarters are the only symbols that can be called "IN" the coat of arms. The shield is being held up by 2 white lions that are called supporters and are part of what is called an "achievement" (complete display) of arms.
As an example, the COAT OF ARMS of the United States of America is white with six red vertical bars and a blue horizontal area at the top. The ACHIEVEMENT OF ARMS of the United States of America has the coat of arms on a shield on the breast of a bald eagle displayed in natural colors with an olive branch in one claw and thirteen white arrows in the other claw. The eagle holds a ribbon with a motto in its beak and there is a "glory" with thirteen white stars on a blue field above the eagle's head.
Thus the eagle is not "ON" the coat of arms because the coat of arms is on a shield on the eagle's breast.
In Edward IV's achievement of arms the white lions are not ON the coat of arms or IN the coat of arms or ON the achievement of arms but are part of and thus more or less IN the achievement of arms.
Someone was nice enough to answer the question you intended to say, but the question that you actually wrote (copying an earlier statement) literally has no correct answer since there are no white animals ON that coat of arms.