Disclaimer:ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€š what I'm about to say is hearsay, so take it FWIW.
None of which is really applicable to the OP or cizinec's question, about which let me give the following direct answer:
OCL's executive leadership is largely composed of Greek lay people, most of whom have no theological training. There are, however, several OCA laypeople on the executive board and at least a few Antiochians in high positions.
After that, the single most influential and outspoken advocate for and participant in OCL activities is His Eminence Archbishop Nathaniel of the Romanian episcopate of the Orthodox Church in America. He sits on OCL's advisory board and has participated in OCL activities. In fact, he recently spent considerable diocesan funds to purchase and create a special center in Detroit called the St. Andrew's House (http://www.orthodoxdetroit.com/
), which is staffed and frequented by prominent members of OCL (including leadership) in the Detroit area. For whatever reason, outside of Chicago and especially in Detroit, most of these members seem to come from the OCA (and then from the Antiochians). Not only was this my impression every time I have visited the center, but the board of St. Andrew's only has one Greek layman on it.
Other than Archbishop Nathaniel, the only other active Orthodox clergy who have had and continue to maintain an official leadership connection with OCL are Fr. Thomas Hopko, Fr. Peter Gillquist and Fr. Gordon Walker.
So, I would say that the OCA actually has more involvement in OCL's leadership, but that certain portions of the Antiochians are well represented.