Curley is being aggressive in this scene, his sense of manly toughness being threatened by Lennie's huge size and strength. Lennie is of course the opposite of what Curley believes, being a gentle giant who wishes no one any harm. Despite his impatience with Lennie, George cares about him a great deal and makes up facts to cover for him when Curley starts getting mean and even suggests he might not want them on as employees.
By saying they're cousins, George is putting off the impression that there might be something amiss about their relationship, since ranch workers typically travel alone. By saying they're cousins, this makes it seem less strange.
George also claims Lennie was hit in the head by a horse because this might sound better to Curley than just explaining that Lennie is mentally challenged. George is doing anything to make sure they get this job in the end.
The lies are also to protect Lennie from Curley's wrath. For all his bluster, George prizes his friendship with Lennie and feels responsible for him. Their strong bond is all that keeps the two men going through their dismal existence as migrant ranch workers.