How to calculate CL with the use of MTOW?
For every equation the left and right side should have the the same units.
For example:

$$ Speed  = \frac{distance \:[m]}{time \: [s]}$$

Or in units:

$$[\frac{m}{s}] = \frac{[m]}{[s]} $$

The same so with the lift equation:

$$L = C_L \cdot \frac{1}{2} \rho V^2 S$$

With units:

$$L [N] = C_L [-] \cdot \frac{1}{2} \: \rho \: \left[ \frac{kg}{m^3} \right] V\left[\frac{m}{s} \right]^2 S [m²]$$

Units only:
$$\require{cancel} [N] = [-] \cdot \left[ \frac{kg}{m^3} \right] \: \left[\frac{m^2}{s^2} \right][ {m^2}] $$
Simplifying:
$$\require{cancel} [N] =  \left[ \frac{kg}{{\cancel{m^3}}} \right] \: \left[\frac{m^\cancel{2}}{s^2} \right][\cancel{ {m^2}}] = \frac{[kg][m]}{[s^2]}$$

Which is correct, link to Wikipedia.

So if you want to use the equation:

$$ L = W $$

Both have to be in $[N]$. You have two options, either have it given to you in Newton, or convert a weight (in $[kg]$) to $[N]$ by using the gravitational acceleration g (in unit $[\frac{m}{s^2}]$ )

I think that the confusion stems from the fact that the unit pound is used in two ways.


for weight called pound (mass)
$$1 [lb] = 0.45359237 [kg]$$ 
for force called pound (force)
$$1 [\mathbf{lbf}] = 1 [lb] \cdot g
   = 4.44 [N] $$


So if somebody is unspecific and asks what the lift is needed to carry 400 pounds, we don't know if it's way 1. or 2.