Sorry out enjoying the sunshine.
In my gazetteer both the Deans in East Sussex are recorded as Eastdean and Westdean i.e. not as separate words.
Westdean is recorded as a hamlet 2 miles south of Alfriston and Eastdean is recorded as a village 4 miles east of Eastbourne. Westdean is closer to Seaford and neither are particularly close to Lewes so may investigate at some point why the SFHG record shows Lewes.
Pheno
The six ancient subdivisions of Sussex known as the Rapes were (W to E) Chichester, Arundel, Bramber, Lewes, Pevensey and Hastings. It may be that Westdean and area was in the rape of Lewes rather than Pevensey, and that was used on occasion to distinguish the places.