The key to forward movement is similar to the backward movement. When they have any significant difference to cover, the players will use the cross step pattern.. Now the first step is forward with the rear foot.
The side on which the rear foot crosses the front foot depends on whether the player is moving forward to the left or right. When the player moves to the right and forward, the rear foot will cross to the right side of the front foot. When moving left and forward, the rear foot will cross to left side of the front foot. In each case, though, the rear foot is stepping towards the net.
Sometimes there is a combination of cross stepping and shuffling after the cross step, depending how far or how fast the player has to move. But, most importantly, the first reaction with your feet is the key. The cross step is what facilitates and maintains the unit turn as a player moves to position for the lob.
The first step to creating a great arm swing, as in all the shots, is creating the turn position with your feet and torso as described above.
Facing the net too much as you prepare for the overhead will restrict acceleration of the racket head. The second step is a good racket drop. As with the serve, the racket falls along the side of the torso with the tip pointing more or less straight down at the court.
The arm swing on the overhead is similar in some ways to the arm swing on the modern serve, and in other ways it is different. At times, the amount of the racket drop on the overhead can be somewhat less than on the serve. This is because the extreme leg drive on the modern serve can increase the external rotation of the shoulder backwards, and therefore increase the lowest point the racket reaches at the bottom of the drop. It's not something to worry about if your arm is just relaxed and you let the racket fall.
In some respects, the movement up to the ball is also the same. The arm motion to the ball begins with the straightening of the elbow and then continues with the turning of the hand to square the racket. These are the same basic mechanisms as the serve, but there with two key differences.
First, as we noted above, you position yourself for the overhead so that, if the ball dropped, it would land on your right shoulder. This position means that the contact point is noticeably more to the right compared to the serve.
The reason for this is that the overhead is usually hit flatter than the serves hit by the same players. Also, because the player is around the service line or even closer, the arc of the shot is more downward into the court.