What are the theoretical limits of ion propulsion? What is the theoretical limit in terms of thrust and energy efficiency a ion thruster can have?
Will they ever be able to lift humans on earth? If so, what would the minimum required conditions to do it?
 A: The theoretical limit is of no concern. There is heavy practical/construction limitation of the thrust level. There would be needed an electronic power source typically 10 times stronger, compared to the power of chemical rocket engine, doing the same thrust task. 
The ion propulsion is intended for weak, long lasting thrust with the minimum of matter to be expelled. It is efficient wrt the mass of the propellent, but not wrt the spent energy. 
The momentum and the impulse as its time derivative grow linearly with the speed of the propellent, but the kinetic energy quadratically. Therefore, with 10 times higher speed of the exhaust, compared to chemical engine, you need 10 times less mass of the propellent, but 10 times more energy.
Typical leaving speed of ions is 50 000 m/s, 1 kg of such matter would have the momentum 50 000 kg.m/s. A person with equipment may have mass cca 100 kg, with weight cca 1000 N. 
As  $$F = \frac{\mathrm{d}p}{\mathrm{d}t}=v \cdot \frac{\mathrm{d}m}{\mathrm{d}t}$$
For the needed 1000 N thrust, we would need the propellent mass flow:
$$ \frac{\mathrm{d}m}{\mathrm{d}t}=\frac{F}{v}=1000/50000=0.02\ \mathrm{kg/s}$$
If ions were made e.g. from hydrogen, 20 g/s would mean circa 20 moles/s of atomic hydrogen. As the Faraday constant is cca 96500 C/mol, you would need the electric current cca 2 MA to lift the person.
Similarly, the needed power  $P = \frac 12 v^2 \cdot  \frac{\mathrm{d}m}{\mathrm{d}t}=50 MW$
As high voltage is easier to provide than high current, there are used rather heavy metallic ions as the propellent. One of good choises is caesium. For M+ ions, e.g. with $M \simeq 100\ \mathrm{g/mol}$ , the needed current/voltage would be 100 times lower/higher, so the needed power $P = U \cdot I$ would remain the same.
Another reason not to do it on the Earth  is to avoid troubles of high speed mass colliding with atmosphere or even ground.
