They say the current Pope died of a stroke when he heard about the loss of Jerusalem and the True Cross relic. The new Pope Gregory VIII of course began his tenure by proclaiming a new Crusade. Loss of the Holy City had been punishment for their sins; Hebrew prophets like Jeremiah could be borrowed for sermons on repentance. Christendom must repent of their luxurious, worldly ways and give an extra tithe to raise a new army.
In Constantinople, the dynasty of the Komnenoi had been overthrown by members of its extended family. The Emperor was now Isaac Angelos, and the plain fact was that Isaac did not want a new Crusade. He wanted to stabilize the local status quo, push back the Seljuk Turks on his eastern side, and accept Saladin. It was hard enough to maintain his own power against palace coups and revolts. He married his sister to a Norman knight to gain European alliances, and that knight (Conrad of Montferrat) then became the guy who took over Tyre in its hour of chaos! So his brother in law ruled Tyre (and by extension, Tripoli), and Greek rites were back in Jerusalem’s churches. Things were pretty good for the Byzantine Empire.
The aging Holy Roman Emperor, Frederick I Barbarossa, set out pretty quickly on his own Crusade. Emperor Isaac actually sought an alliance with Saladin, terrified that a new wave of Latin trouble was coming. The German army arrived on Byzantine territory and asked permission to cross, but the Emperor tried to block them. The Germans occupied a Greek city and defeated the Byzantine army sent to remove them. So that’s about how the Third Crusade started out, as to cooperation. It worked out badly for Emperor Isaac, too; his power dwindled until finally a coup removed and blinded him.
The Germans didn’t get far. In June 1190, the Holy Roman Emperor’s horse slipped on a rock while crossing a river in Turkey. He died, and here we get those horrible royal burial details again. His son had the flesh boiled off his bones, so that the bones could go on with them to the Holy Land, fulfilling his oath. With difficulty, the remaining Germans brought the bones to Tyre, where cousin Conrad helped bury them in Acre.
Meanwhile, the really spectacular part of the Third Crusade was still ramping up, back in England and France. Henry II thought he’d join and started taxing England for the Crusade, but he died. That left Richard being crowned midway through the taxing process, inheriting the mission. Richard was all too happy to leave London as soon as possible and head out on a war adventure. He had been working on overthrowing his father with France’s help; now he joined the Crusade with his dear friend, the French King Philip II.