Richard the Lionheart was very popular with the common people and was considered a very good man who spent most of his time fighting for the cause of his religion, thus making him a better warrior than a king. With regard to the Canterbury Tales, Richard could be compared to the Knight--one of Chaucer's three "good" characters. The Knight is a good man with a pure heart who spends much of his time fighting for his religion as well. He is truly going on the pilgrammage for spiritual reasons unlike most of his companions.
I am not sure exactly what you are looking for, but I can certainly give you some background on Richard the Lionheart and the Crusades. Richard along with Philip Augustus of France, led the Third Crusade to the Holy Land. While the First Crusade had been a wild success establishing the Latin Kingdom of Jerusalem, the conquest had united the Muslims together to wrest back the Holy land from the Christians. The Second Crusade was an utter disaster and Jerusalem fell back into the hands of the Muslims. The Third Crusade was fought against the Muslim leader Saladin. Richard after leading the Christian Troops to victory at Acre, realized that total victory was not possible so he negotiated with Saladin so that while Jerusalem would remain in Muslim hands, it would be open to Christian pilgrims. During the negotiations, it was suggested that Richard's sister marry Saladin. Richard was in many places vilified for negotiating with Saladin. On the way home he was shipwrecked three times and held hostage by Leopold of Austria. Of his ten years of rule in England, Richard spent only six months in the country.