Douglas Richardson given gives reason for not citing William’s death as “1 May 1236”. In his Magna Carta Ancestry, v.1, Richardson sources William as living in 1242. He then gives 4 Sep 1242 as the date of death.
Round (probably), as sourced in the DNB, Vol 1 bio shows only “d.1236” as William’s death year as does The Magna Carta Project webpage.
All About History’s website, reliant on the Biography of William D'Aubigny 1151-1236, states: “On 06 May 1236 William D'Aubigny (age 85) died at Uffington, Leicestershire. His remains were buried at Newstead Abbey, Nottinghamshire with his heart being buried at Belvoir Priory.” Only with access to the book can one learn if there a source to support the date. The Denis Gouey Bookbinding Studio webpage titled The Twenty-five Barons Appointed to Enforce the Magna Carta concurs that “William d’Aubigny or D’Aubeney, Lord of Belvoir (died 1 May 1236)”, but upon which source it relies is anyone’s guess.