To my knowledge, I don’t know of the connection between the two. As you know lateral epicondylitis is as an overuse injury from repetitive flexion and extension at the wrist, hence, the tennis elbow.
The best way to recover from that is to A) stop the trauma by limiting the repetitive motion, B) talking anti-inflammatories and ice to reduce the inflammation and C) build strength and ROM at the wrist.
Anemia is a completely different topic over all, there are two types of anemia vitamin deficiency or iron (mineral) deficiency. There have been studies to suggest that competitive female athletes have also suffered from anemia (amongst other issues) due to overexercise. You can read more about the female athlete triad here:
But no, I don’t know anyone who has made the leap to suggest that the lack of iron absorption (which results in anemia) could help/hider recover patients from tennis elbow.
Hope this helps.
Denise Lee, MES