Lysanias in Wikipedia
Lysanias was the ruler of a small realm on the western slopes of Mount Hermon, attested to by the Jewish writer Josephus and in coins from circa 40 BC. There is also mention of a Lysanias dated to 29 AD in the gospel of Luke. It has been debated whether these are the same person.
Lysanias in Josephus
Lysanias was the ruler of a tetrarchy, centered on the town of Abila. This has been referred to by various names including Abilene, Chalcis and Iturea, from about 40-36 BC. Josephus is our main source for the life of Lysanias.
His father was Ptolemy son of Mennaeus who ruled the tetrarchy before him. Lysanias was cousin of Antigonus, who he helped during the latter's attempt to claim the throne of Judea in 40 BC with the military support of the Parthians.
According to Josephus (B.J. 1.248), he offered the Parthian satrap Barzapharnes "a thousand talents and 500 women to bring Antigonus back and raise him to the throne, after deposing Hyrcanus". However, Josephus in his later work, the Jewish Antiquities 14.330-331, relates that it was Antigonus who made the offer to the Parthians. Whichever the case, Lysanias was put to death by Mark Antony for his Parthian sympathies, at the instigation of Cleopatra, who had eyes on the territories of Lysanias.
Coins from his reign indicate that he was "tetrarch and high priest". The same description can be found on the coins of his father, Ptolemy son of Mennaeus and on those of a possible near relative Zenodorus who held the territory in 23-20 BC.
Lysanias in Luke
The Luke 3:1 records that a Lysanias was tetrarch of Abilene in the time of John the Baptist.
According to Josephus the emperor Claudius in AD 42 confirmed Agrippa I in the possession of Abila of Lysanias already bestowed upon him by Caligula, elsewhere described as Abila, which had formed the tetrarchy of Lysanias. The statement appears in the Wars:
"He added to it the kingdom of Lysanias, and that province of Abilene" 
and also in Antiquities (Ant. xix.5, 1).
Two inscriptions have been ascribed to Lysanias. . The name is conjectural in the latter case.
The first, a temple inscription found at Abila, named Lysanias as the Tetrarch of the locality.
Huper tes ton kurion Se[baston] For the salvation of the Au[gust] lords
soterias kai tou sum[pantos] and of [all] their household,
auton oikou, Numphaios Ae[tou] Nymphaeus, free[dman] of Ea[gle]
Lusianiou tetrarchou apele[utheors] Lysanias tetrarch established
ten odon ktisas k.t.l this street and other things.
It has been thought that the reference to August lords as a joint title was given only to the emperor Tiberius (son of Augustus) and his mother Livia (widow of Augustus) . This reference would establish the date of the inscription to between A.D. 14 (when Tiberius began to reign) and 29 (when Livia died), and thus could not be reasonably interpreted as referring to the ruler executed by Mark Antony in 36 BC. However, Augustus and Livia together were referred to during their lifetimes as SEBASTWI, ie Augusti, so there is no reason to assume this fragment should be dated as late as the reign of Augustus.
Possible identity of the two figures
There is some debate over whether these sources refer to the same person, or two different people.
Some say that the Lysanias whose tetrarchy was given to Agrippa cannot be the Lysanias executed by Antony, since his paternal inheritance, even allowing for some curtailment by Pompey, must have been of far greater extent. Therefore the Lysanias in Luke (AD 28-29) is a younger Lysanias, tetrarch of Abilene only, one of the districts into which the original kingdom was split up after the death of Lysanias I. This younger Lysanias may have been a son of the latter, and identical with, or the father of, the Claudian Lysanias.
But Josephus does not refer to a second Lysanias. It is therefore suggested by others that he really does refer to the original Lysanias, even though the latter died decades earlier. In BJ 2.215 Josephus refers to the realm as being "called the kingdom of Lysanias", while Ptolemy writing circa 120 AD in his Geography Bk 5 refers to Abila as "called of Lysanias"
The explanation given by M. Krenkel  is that Josephus does not mean to imply that Abila was the only possession of Lysanias, and that he calls it the tetrarchy or kingdom of Lysanias because it was the last remnant of the domain of Lysanias which remained under direct Roman administration until the time of Agrippa.