He was a son of Eustace fitz John (died 1157), hereditary Constable of Chester, by his second wife Agnes, daughter and eventual heiress of William fitz Nigel (died 1134), of Halton Castle, hereditary Constable of Chester and feudal Baron of Halton.
Richard fitz Eustace in turn inherited the barony and constableship.
[1][better source needed] During the reign of King Henry II, Richard held one knight's fee in Smathe, Yorkshire.
[2] The de Lacy family took its name from the manor of Lassy in Calvados, Normandy.
[2] Albreda de Lissours survived her husband and remarried to William FitzWilliam, by whom she had further children.