Which Leo are you referring too exactly? it gets a bit confusing due to Cilicia being a principality from 1080-1198 and then a kingdom from 1198-1375. So the kings after 1198 where both the first and the second if they took the name of an older king, for example Leo II was also Leo I as he was the first king of Cilicia after it became a Kingdom from 1198 but also the second as there was a Leo before him than ruled from 1129-1140 when it was still a principality. Leo I and Leo I (II) where of the Rubenid Dynasty while Leo II (III) was of the Hethumids. What gets more confusing is that most Cilician kings had about three separate names, for example Leo I (II) was also called Levon or Leon, both an Armenian and European sounding name i guess.
if you look at the wiki article it show how the Cilician monarchs where numbered.
https://en.wikipedia.org/wiki/List_o...dom_of_Cilicia