How does a lack of emotion result from anorexia?

Anorexia and emotion. Your question perhaps needs to be reversed, since emotions can play a significant role in anorexia. Talk to your family doctor, and consider also talking with a psychiatrist or clinical psychologist.
See below. In addition to the effect of starvation on brain function, brain imaging data suggests that the brain of someone with anorexia is unable to distinguish a reward from a loss. As food reward is processed by this system, deriving pleasure from eating is not "natural" in them.
The brain. Lack of emotion, or dysregulated emotion, occurs frequently when the brain has been starved. If the starvation is of long enough duration, apathy and indifference to one's surroundings sets in. This is also seen in famines and with intentional starvation in times of war. Children are especially vulnerable to this, but adults are affected too.

Related Questions

Can you tell me how can a lack of emotion or flat mood result from anorexia?

Depression. Lack of emotion and flat mood can result from depression that can come along with anorexia nervosa. Also if the patient is sick enough -- malnourished, purging, weak, etc -- s/he can be apathetic as well. Read more...
Complex Relationship. There is a complex relationship between emotions and anorexia. Anorexia is, in fact, an emotional disorder that stems from a wish to be at a "perfect" weight, one that will guarantee love and freedom from pain. This obsessional focus distracts from or masks other, generally darker and more depressive feelings. What's left is obsessional anxiety, relentless pursuit, or nothing. Read more...