Lucas de Viene (also spelled Vyenne) was a lord of two manors in Sussex, Putwood and Cudlow. He also apparently had enough of a rivalry with John de Bohun that the latter and several of his servants ambushed the former and ducked him in a horse pond.
Blazon: Per pale argent a pall gules and of the last, a Maltese cross of the first, pointé in base barry wavy of the first and azure
Although Ruidera fell into the territory of the Order of Santiago (per a 1237 treaty), it ultimately ended up as the property of the Order of St. John in 1783, which is probably the source for the Maltese cross. There are also many lagoons and wetlands in the area under national protection, which may be the source of the barry wavy point.
From p122 of Lacies Nobilitie by Sir John Ferne (1586)
Blazon: Per quarterly I and IV or and gules a bend sable and a label of three points argent (Lacy), II and III or a lion rampant purpre (Cotentin)
Roger received the castle and barony of Pontefract through Albreda de Lisours. (Ferne has her as Roger’s mother, but other sources point to her as his grandmother; I am not sure of their exact relationship.) He was not born a Lacy; his father, John fitz Richard, was the baron of Halton and grandson of Nigel de Cotentin. Roger assumed the Lacy name and arms as a condition of his succession to the properties of Pontefract.
Blazon: Per fess argent a castle gules windowed or and of the last a bend wavy azure
The castle may be either a reference to or a representation of one of two local castles; the castle of Prim, a military residence that once hosted a meeting between Juan Prim y Prats and Pope Pius IX, or the castle Milagro (Castle of the Miracle) which was built by Rodrigo Jiménez de Rada during the Reconquista.
Blazon: Per quarterly I and IV azure a bend of five lozenges conjoined or, II and III per pale indented or and gules, overall on a cross ermine a mitre proper
Crest: On a wreath or and azure issuant from a mural crown or charged with a Tudor rose a dexter arm embowed holding a hammer all proper
Supporters: On the dexter a figure representing Art proper vested argent wreathed with laurel vert tied by a riband gules, holding in the sinister hand resting on the shield a book bound of the last and in the dexter a palette with two brushes proper; on the sinister a figure representing Industry habited as a smith, holding in the dexter hand resting on the shield a cupel and in the sinister a hammer resting on an anvil all proper
Mantling: Azure lined or
Both coats quartered here were used by the de Bermingham family at various points in time. The family also quartered the coats, but in opposite quarters; the city changed the order for difference. The city was previously granted arms in 1889, which used a fess ermine instead of a cross, and a mural crown instead of a mitre. The supporters in the previous arms were also reversed, with Industry on the dexter and Art on the sinister.