As far as I know, there was no Byzantine participation in the Reconquista, or at least no official participation. The Byzantines did not subscribe to the religious/ideological aims of the crusaders and from the very start there was friction between them and the Crusaders. The Crusaders were resentful for not receiving the assistance they thought was due to them, and the Byzantines were resentful that the Crusaders pillaged their way through Byzantine lands that they were ostensibly there to defend. And of course the Byzantines themselves were on the frontlines, so to speak, of Christendom against Islam. Their resources were devoted to keeping their own territories intact.

Practically, getting to Iberia would mean a stopover in the Norman Kingdom of Sicily, which was extremely unfriendly to the Empire ever since the Normans conquered the Mezzogiorno in the late 11th century. In the 1150s, the Byzantines returned and actually made startlingly rapid gains before ultimately being pushed back. I would think the Normans would be reluctant to help a Byzantine fleet on its way to Spain, especially since it could have easily been a ruse to stage an invasion. Subterfuge being a Byzantine specialty.

I believe that Lisbon was conquered with assistance from English Crusaders on their way to the Levant, but hopefully a Reconquista expert will come along to give you the whole story.