Answer: The main conflict that exists between Arthur and Lancelot is because Lancelot is in love with Guinevere, Arthur's wife. This is made slightly more complicated by the fact that Arthur is the King and Guinevere the Queen, so technically Arthur can mete out justice if he determines Lancelot has broken the law.
The answers are Linton (the family of Thrushcross Grave is called Linton)and Desire (she craves Heathcliff, but she desires the status that comes with nobility)