Place celery root, 1/2 of the lemon juice, and kosher salt in a large pot and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender, 15 to 20 minutes. Drain.
Blend celery root, cream, and butter in a blender until smooth. Push puree into a bowl through a fine-mesh strainer with a wooden spoon or spatula until puree is completely smooth. Drizzle remaining lemon juice into puree and season with salt and cayenne pepper.