The greater variant has a dynastic inescutcheon with the arms of the House of Bourbon-Parma (Blazon: Azure bordure Gules charged with eight escallops Argent, three fleurs-de-lys Or).
The supporters are holding a lance Or, flying the flag of the Netherlands, all surrounded by ermine mantling with the crown.
The greater arms featuring the former territorial claims attached to the duchy of Nassau that was annexed by Prussia in 1866 were, however, unreflective of political reality of the time and were not used extensively: They were only used on the Great Seal of Grand Duke Jean.
In such a case, the choice of colour of the bars would have been selected to match the white field and red lion of Limburg.
The relationship is unknown, if indeed any exists at all although the link between the Lusignan and Luxembourg coat-of-arms is provided in 'Le Roman de Mélusine' by Couldrette whereby a descendant of the legendary founder and faerie queen of Lusignan adopts the burely of 10 argent and azure, adding the lion rampant due to his similarly shaped birthmark.