How to use Mathf.Lerp and Mathf.InverseLerp???

It's not clear what your agenda with altering weight is, you might be able to use crossfade between states instead:

 yourAnimation.blendMode = AnimationBlendMode.Additive;
 animation.CrossFade("yourAnimation", 0.1);

Have a look at how it's possible to do crossfading between different animation-states here (using Animation Layers). The Character Animation is very helpful from the Manual and also see the Script Reference for Animations.

There are a couple of Mathf functions you could use for interpolating values,

 yourAnimation.weight = Mathf.SmoothStep(0.0, 1.0, Time.time);
 yourAnimation.weight = Mathf.SmoothDamp(yourAnimation.weight, 1.0, 0.0, 0.3);
 yourAnimation.weight = Mathf.Lerp(yourAnimation.weight, 1.0, Time.time);

Then you could use an if-statement to just go between min and max:

 if(Input.GetAxis("yourAxis")){
     yourAnimation.weight = Mathf.Lerp(yourAnimation.weight, 1.0, Time.time);
 }else{
     yourAnimation.weight = Mathf.Lerp(yourAnimation.weight, 0.0, Time.time);
 }

Have a look at Mathf in the script reference for more details.

Does any of these solutions seem helpful for your situation?