Lerp incomplete movement problem

Hey guys, I'm working on a project where the player toggles movement directions with the keyboard, and their controllable character moves in fixed increments, as if in a grid. Each 'grid tile' is to be 1x1.

I've read the GridMove script on the Wiki site, but it's not compatible with with the movement limitations the game mechanics will employ. As a result, I've used Vector3.lerp to create a simpler version, but I need the player to move uninterupted, wheras the movement stops once the player is no longer holding down the key. I need it to move 1 'unit' along the X axis (other directions can come later) when the button is pressed. It is critical that the player only moves one whole number at a time. If anybody can help me figure out what I'm doing wrong, it'd save me further headache!

here's what I've stripped my previous system down to:

var startPosition : Vector3; var endPosition : Vector3;

 startPosition = myTransform.position;

     //Detect left or right movement
 horizontalMovement = Input.GetAxis("Horizontal");

 //Detect up or down movement
 verticalMovement = Input.GetAxis("Vertical");   

 if (horizontalMovement > 0 ){
     MoveRight();
 }

     endPosition = Vector3(myTransform.position.x+1.0,myTransform.position.y, Time.deltaTime);
     myTransform.position = Vector3.Lerp(startPosition, endPosition, Time.deltaTime);

}

Cheers, - Stew