What is the maximum theoretical lift of a plane as a function of engine power and surface of the wings?
Your thrust equation is only valid for the static case (initial speed at infinite distance from the propeller is zero), and neglects the propeller's efficiency. For the flight case, I recommend to make a bold assumption for propeller efficiency and to assume that most power will be converted to thrust:

$$T = \frac{P}{v}\cdot\eta_{Prop}$$

A large, slowly turning propeller will have an efficiency approaching 90%, while a small, fast-spinning one will only reach 70%. If operated outside of its design speed, efficiency might even become negative. If you look for an upper boundary of thrust, the equation above sans efficiency will do nicely.

For the maximum lift answer you should expand your drag coefficient a little, as recommended already in this answer. $$c_D = c_{D0} + \frac{c_L^2}{\pi\cdot AR\cdot\epsilon}$$

Now you can equate drag and thrust to get: $$P\cdot\eta_{Prop} = \left(c_{D0} + \frac{c_L^2}{\pi\cdot AR\cdot\epsilon}\right)\cdot S\cdot\frac{\rho}{2}\cdot v^3$$

and solve for lift: $$L = c_L\cdot S\cdot\frac{\rho}{2}\cdot v^2 = \sqrt{\pi\cdot AR\cdot\epsilon\cdot\left(\frac{P}{v}\cdot\eta_{Prop} - c_{D0}\cdot S\cdot\frac{\rho}{2}\cdot v^2\right)}\cdot\sqrt{S\cdot\frac{\rho}{2}\cdot v^2}$$

The minimum power is consumed when the ratio $\frac{c_L^3}{c_D^2}$ reaches its maximum. Expressed differently, this means that $$c_L = \sqrt{3\cdot\pi\cdot AR\cdot\epsilon\cdot c_{D0}}$$

Plugging that back into the lift equation I leave as an exercise to the reader.

As you can see, the answer really depends on the aerodynamic quality of your airfoil. The best you can reach with regular airfoils is a $c_L$ between 1.5 and 1.8, depending on Reynolds number. With slotted flaps this can be doubled, but $c_{D0}$ will go up substantially, so the best ratio $\frac{c_L^3}{c_D^2}$ can be gained with a clean airfoil.

Nomenclature:
    $c_L \:\:\:$ lift coefficient (normally between 0 and 1.5)
    $S \:\:\:\:\:$ Wing surface area
    $\pi \:\:\:\:\:$  3.14159$\dots$
    $AR \:\:$  aspect ratio of the wing (ratio of span to mean chord)
    $\epsilon \:\:\:\:\:$  the wing's Oswald factor (use 0.8 when in doubt)
    $c_{D0} \:$  zero-lift drag coefficient (use 0.02 when in doubt and 0.03 with a fixed gear)