Try this scale demo. Put it on a cube or something. As you press Fire1 (left mouse button), the object change scale from 1 to 2 and back again next time. It uses coroutines to interpolate scale between two values with an adjustable speed.

var speed : float = 5.0f;

function Start()
{
    yield Demo();
}

function Demo()
{
    while (true)
    {
        yield WaitForButton("Fire1");
        yield ScaleRoutine(transform.localScale, Vector3.one * 2.0f, speed);
        yield WaitForButton("Fire1");
        yield ScaleRoutine(transform.localScale, Vector3.one, speed);
    }
}

function WaitForButton(button : String)
{
    while (!Input.GetButtonDown(button))
        yield;
}

function ScaleRoutine(fromScale : Vector3, toScale : Vector3, speed : float)
{   
    // Basic error handling.
    if (speed <= 0)
    {
        Debug.LogError("speed must be > 0 or algorithm would loop forever");
        return;
    } 

    var scale = fromScale;
    while (transform.localScale != toScale)
    {
        var move : float = speed * Time.deltaTime;
        scale = Vector3.MoveTowards (scale, toScale, move); 
        transform.localScale = scale;
        yield;
    }
}

This function needs to be in Update(), then it sould work. The Lerp will interpolate any value in localScale smoothly to the new absolute value "newScale". The only thing than can influence this is (assuming you don't have any stray scripts messing with your values), that any of the parents have scales other than 1 that keep changing.

localScale is absolute; it's not relative. Using Vector3.Lerp like that won't accomplish anything, however. The third parameter in Lerp is a float between 0 and 1, so assuming you want an animation of the scaling, you need to make a routine that animates the third parameter from 0 to 1 over time. See this for examples of coroutines which you could easily adapt to use localScale rather than position or rotation.