Answer:
From the lines that are available in the question, the ones that describe more explicitly his participation in the Crusades are:
“This self-same worthy Knight had been also
At one time with the lord of Palatye…”
Here he is described as having served the lord of Palatye. Palatye is the Middle English version of the word Palathia. Palathia was a Christian fief in Asia Minor (modern Turkey). When the Crusaders went to Asia Minor on their way to liberate the Holy Land from Islamic invaders, they established several Christian lordships along the route in order to protect Christian pilgrims from Europe on their way to Jerusalem. Palathia was one of such lordships and it was located in Asia Minor, in what had been part of the Christian Byzantine Empire and had been invaded and conquered by Muslim Turks.