Atopic eczema is a primary inflammatory condition, whereas lichen simplex chronicus is a secondary, localized, thickened plaque that results from the chronic rubbing and scratching of any underlying itchy condition.
Hypertrophic lichen planus can be very thick and itchy, but it arises from primary violaceous papules, unlike lichen simplex which arises from non-specific chronic scratching.
This is a symptom (anal itching) which can lead to lichen simplex of the perianal skin, not a differential diagnosis of the skin change itself.
Scabies is the primary infestation that can cause the itch leading to lichen simplex, and is diagnosed by finding burrows or mites.