Is work done dependent on velocity?
I wasn't going to post an answer to this, but the other answers seem very insufficient to me and may give the wrong idea.
The work required to lift an object off the ground is not affected by velocity directly. The work is proportional to the product of the force acting on the object, and it's displacement in the direction of that force.
This means that if you are applying the same force over the same distance, it takes the same amount of work, regardless of the velocity.
The velocity is relevant to the power required; which is energy per unit time. The faster you want to travel the displacement, the more power is required, so you need to deliver the same amount of energy in a decreased time frame.
You talk about overcoming gravity in the comments, and I will try to clear up confusion there as well. If gravity increases, to overcome gravity you would need a greater minimum force to overcome it's effects. Because of this, an increase in gravity will lead to an increase in required force for the same results, and if that force increases, the required work would increase as well.
So to reiterate again, velocity has no direct bearing on the applied work. It will affect the required power, but the amount of work required to move the specified distance only depends on the displacement and the applied force; not upon how quickly it travels the displacement.