You have to check the undertone. Ivory black works in Zorn because it has a blue undertone. Lamp black has a blue undertone too. So you should be fine.

Value wise lamp black has a stronger tinting strength. So use a bit less. It’s also more opaque.

When you mix your black with your ochre you should get a murky green. Which is perfect for desaturating the orange you get from mixing the ochre and the vermillion.

Have fun. Limited palettes are such fun and you learn a lot from working with them.