AnalogRead unstable with ColorLCD

So I think maybe there are some kinds of capacitors (the varying has... constent cycles) in the LCD which are perturbating the inside of Arduino ??

No I would not think so.
It is the very lack of capacitors that is causing you the problem.

First make sure your power supply can delver the expected current. Then add a 10 to 100uF capacitor across power and ground of the LCD.