Richard Fitz Lewis has a page on the history of parliament website, and a Wikipedia stub article. His family is discussed for example here, here and here. He had four wives, so it is difficult to determine which was the mother of each child.
Richard's father was Lewis fitz Lewis, apparently sometimes also referred to as Lewis John (he apparently chose the new surname). He was a Lancastrian allied with Thomas Chaucer. (During the York regime, the family lost its inheritance.) This Lewis died in 1471 at the battle of Barnet. Old books (maybe Morant, the old historian of Essex, is the first) say his wife was Margaret Stonor.
Richard's grandfather was a London businessman and vintner, apparently of Welsh origin, referred to as Lewis John or John Louis, who also has a history of parliament article. Lewis John married well. His sons were apparently from his first wife, Alice de Vere, daughter of Aubrey de Vere, 10th earl of Oxford (Wikipedia, OBNB, Medlands) by Alice Fitzwalter, daughter of John, Lord Fitzwalter, (and widow of Sir Francis Court of Tytherley). These FitzWalters are the ones descended from Walter FitzRobert (Medlands), and his wife Ida de Longspee, grand-daughter of King Henry II, and William FitzPatrick the Earl of Salisbury.
Have you taken a DNA test for genealogy? If so, login to add it. If not, see our friends at Ancestry DNA.