en.wikipedia.org/wiki/House_of_Lusignan

This caption overstates Lusignan rule.

A standard reference entry on the Lusignan family says the crusading branch produced kings of Jerusalem and Cyprus, and later a branch took the throne of Lesser Armenia (Cilicia). It does not list Antioch or Tripoli among Lusignan-ruled states.

Separate reference works on the Crusader states identify Antioch as a principality established by Bohemond of Taranto and Tripoli as a county founded by Raymond of Toulouse / Raymond of St. Gilles. Another reference on the Crusader states adds that after 1187 Antioch and Jerusalem remained independent of one another, while Bohemond IV controlled Tripoli; that is not Lusignan rule.

So the Lusignans did hold the kingdom of Jerusalem at points, but saying they also ruled the Principality of Antioch and the County of Tripoli is incorrect.

The chronology and the standard modern account do not support Richard as the person who drove Aimery out.

Peter W. Edbury's Cambridge history of the Lusignans states that Aimery, Geoffrey and Guy had all been involved in rebellions against Richard's father, King Henry II, with Aimery's rebellion in 1168, and that Aimery left for the East soon after his rebellion, being already a vassal of Baldwin IV by 1174. That directly contradicts the article's statement that Aimery had been expelled by Richard.

A municipal history of Lusignan gives the same local context for 1168: it says Henry II had the Lusignan castle razed in reprisal for the killing of Patrick of Salisbury. So the conflict that drove the family from favor was with Henry II's regime, not an expulsion by Richard the Lionheart.

In short: the evidence points to Aimery leaving after a rebellion against Henry II, not after being expelled by Richard.

Local official histories contradict this claim.

The municipal history of Lusignan says the fortress was dismantled in 1575 on the orders of Henri III, and that the Tour Mélusine, preserved for a time, was destroyed in 1622 on Richelieu's orders. That places the effective destruction of the castle under Henri III / Louis XIII, before Louis XIV's reign even began.

The Tourisme Vienne page likewise describes Lusignan today as the vestiges of an imposing fortress dating from the 10th to 16th centuries. So the site surviving into the modern period as ruins fits the municipal account; it does not fit a claim that Louis XIV fortified it.

Because the castle had already been dismantled before Louis XIV ruled France, attributing fortification of the château to Louis XIV is incorrect.

This statement conflicts with the documented end of Lusignan rule in France.

The municipal history of Lusignan states that the Lusignan dynasty died out in 1303 and that Philip IV attached its lands and possessions to the French crown in 1314. That directly contradicts the claim that a 'principal branch' still retained Lusignan and the County of La Marche centuries later.

A general reference entry on the family likewise says the Lusignans ruled the county of Marche in the 13th–14th centuries, and that the dynasty itself ultimately ended with James III in 1474. So the article's claim about an 18th-century principal branch still holding Lusignan/La Marche is not compatible with the historical succession of the family or of the territory.

In other words: Lusignan and La Marche had ceased to be held by a ruling Lusignan branch long before the 18th century.