Res-Scaling method beats PID controller. How?

How is the (P) controller not standing up to its task ?

Well, just like you said - how is it not standing up to its task? What is it doing that makes you think it's not working? You said,

I tried multiple values of Kp but could not succeed

Nobody here knows what that means. "Could not succeed" could be a lot of problems. My guess is that you're trying to regulate something with only a proportional controller. Integral gains are the only way to drive steady-state error to zero.

What are some other things you could be doing wrong? Well, for starters, you said:

I am trying to control the the position of the arm [so]... it moves more when far and less when near [the table].

This sounds like you want a signed error, to drive your arm in two directions, yet your code you provided has error calculated as:

error = abs(200 - LIDAR_1)

If your error only has one sign (positive) then your arm only moves in one direction. Also, your error is calculated only with LIDAR_1, even though your entry into that calculation depends on LIDAR_1 and LIDAR_2. Are you sure that you don't want something like

error = LIDAR_2 - LIDAR1

or something similar? You haven't provided any diagrams showing what your values are, what the significance of 200 is, what angle it is you're trying to control, or how you're calculating that angle.

Next, following your code all the way through:

error = abs(200 - LIDAR_1)
duration = error * Kp
# To keep everything < 1.0 
factor = factor%1.0
arm_down(factor)

Let's look at your code line-by-line:

1. Calculate the (absolute value of an) error,
2. Modify the error with a proportional gain to make a "duration,"
3. Modify a "factor,"
4. Use the factor to run arm_down.

Note: At no point in there did you use the duration. Maybe you meant factor = duration % 1.0?

But, finally, modulus is not your friend. This is definitely NOT what you want for it to be doing.

On the topic of the modulus, you said

to scale the range (given by the lidar) to the desired range (0.1 to 5.0). To filter very high values, I used a mod operator a.k.a % in Python.

First, you say that you want the desired range to be 0.1 to 5.0, but you're doing value % 1.0, so you're only going to get numbers between 0 and 0.999.

Second, you're making your control signal "wrap." Assuming you actually did value % 5.0, which I think is what you were intending given your stated desired range, then you get the following:

4.8 % 5.0 = 4.8
4.9 % 5.0 = 4.9
5.0 % 5.0 = 0
5.1 % 5.0 = 0.1
5.2 % 5.0 = 0.2

If you think of this like a cruise-control system, a very fast acceleration would have you push the pedal all the way to the floor, but if you wanted to accelerate even faster then your modulus operation actually has the controller take its foot completely off the pedal.

What you need instead is to clamp the value, like

if(duration > 5.0)
    duration = 5.0

The best thing you can do for us, and yourself, is to make a drawing that shows where your lidar units are, what measurement you're expecting from them, and how those measurements relate to an angle you're trying to control.

You should then calculate that angle, using the diagram as a guide for developing the equation, and use the angle instead of raw lidar readings in your code.

Finally, structurally speaking, your PID/controller code should accept the angle/error and use that to calculate a raw control signal. If you have some downstream process that needs it to be in a particular range, then you can modify/saturate/clamp that signal inside that downstream process. This keeps your code more modular and easier to troubleshoot.