Do coaxial rotors provide twice the amount of lift?
What about the engine? Even if engine power was doubled, the coaxial rotor won't produce double the lift.
Airfoils don't like stacking neighbors.
(Source)
This double wing above (biplane) produced about 120% lift, not 200%.
Using the biplane above to illustrate a point, between the wings the pressure will neither be high enough for the upper wing, nor low enough for the lower wing.

In a biplane aircraft, two wings are placed one above the other. Each provides part of the lift, although they are not able to produce twice as much lift as a single wing of similar size and shape because the upper and the lower are working on nearly the same portion of the atmosphere and thus interfere with each other's behavior.

For the same engine output, we're looking at ~10% increase in lift.

Because the coaxial rotor does not require an anti-torque device such as a tail rotor, Fenestron, or Notar, a coaxial rotor helicopter requires about 10% less power than a single rotor/tail rotor helicopter.
For the same rotor diameter and power the coax will lift approximately 11% more weight. This equates to 30% greater useful load, which means more payload or fuel. The coax helicopter can hover at a 6000 ft higher altitude, or at a higher temperature (avxaircraft.com).