According to LMX Theory, most leaders try to treat each subordinate the same way to ensure fairness?

That is correct to an extent. The leader is willing to give each subordinate a chance to demonstrate his or her capabilities. Based on how well they do on the test they will be put into an in group or an out group. Also if the subordinate doesn't support the leader they will fail the test regardless of their abilities. The in group is the group of people that the leader relies on the most and gives special treatment too. So if it is an organization these people may eventually get promoted. The out group is made up of the subordinates that the leader does not rely on usually because they aren't kissing the leader's or they aren't doing a good job. These people aren't going anywhere in this organization.