Can lasers lift objects?

Your approach is incorrect. You cannot do this calculation by considering that the energy absorbed by the object is converted into a change in gravitational potential energy. For one thing the object would just get hot and radiate away most of the energy and for another this is a dynamical problem, you have to be able to accelerate the object upwards.

What is important is the product of the power per unit area of the laser and the area over which it is incident. More precisely, to "levitate" an object by shining a laser onto its underside requires that the force exerted upwards by the laser is equal to the force $mg$ acting downwards. A general expression one could use is $$\frac{1+r}{c}\int \vec{S} \cdot d\vec{A} \geq mg,$$ where $\vec{S}$ is the time-averaged Poynting vector of the laser, with a magnitude equal to the power per unit area in the beam, and the component of this normal to the surface is integrated over the surface area of the object to be levitated. The term $r$ is the reflectivity of the surface. $r=0$ for a black surface, but the upward force would be doubled for a perfectly reflective surface with $r=1$.

Hence assuming I had a completely black cube of surface area $A$ oriented so that a surface was perpendicular to a laser beam with Poynting vector $S$: $$ \frac{SA}{c} \geq m g$$ $$ m \leq \frac{SA}{cg}$$ and if $SA = 1$ W, then $m \leq 3.4 \times 10^{-10}$ kg is the mass which it could accelerate upwards against gravity.

Your consideration implies you have a device that can convert laser light with 100% efficiency and convert it to mechanical power. This is theoretically possible, but there is not much of physics. You still need some ladder to climb along, and building a space elevator requires much tougher materials than we currently know.

In practice, you would have to use some nonideal conversion mechanism, e.g. a photovoltaic panel. With the state-of-the-art technology, you can get to roughly 40% efficiency; the mechanical part of your device can be made fairly efficient, so we can expect your laser could provide power for 1/3 m/s climbing speed with a 100 gram weight of the device. Seems possible.

Without any ladder, you can use a very powerful laser to exert direct optical pressure. If you divide the momentum of any photon by its energy, you arrive to the fact that 1000 mW laser exerts a 1/c=3.3 nN pressure on any absorbing surface. Provided the light would be fully reflected, you would need a continuous 150 megawatt laser to lift a 100-gram mirror. This is three orders of magnitude more power than what we have built so far, although the total power requirements could be significantly reduced if a mirror was added on the launchpad to form a giant optical resonator.

Another option would be to use a less powerful laser to heat up some evaporative bottom of the rocket, so that it does not have to bring all its energy in the form of relatively inefficient fuel. This appears as one of plausible ways for rocket propulsion of the future.

Lookup Optical Tweezers.

The limitations of the technique are due to the damage thresholds; see laser ablation.

This idea has been used extensively in science fiction, especially when implemented as solar sails. It's even practical for some applications, as noted in the article. But laser propulsion from the ground suffers losses due to the atmosphere.

The photonic laser thruster is the hot new technology.