Note the Work-Energy Theorem, which gives that

the work done by all forces acting on a particle equals the change in the particle's kinetic energy + the change in the particle's potential energy.

In your case, kinetic energy is unchanged but potential energy isn't. Assuming the floor as a zero point, the change in potential energy is $mg\Delta{h}$, which is our answer, 2600J.

Finally,

But what's stopping me from saying the object has a constant velocity of zero which would mean the barbell would never move?

The fact that Lamar lifts the weight means it does not have a constant velocity of 0.

Note the Work-Energy Theorem, which gives that

the work done by all forces acting on a particle equals the change in the particle's kinetic energy + the change in the particle's potential energy.

In your case, kinetic energy is unchanged but potential energy isn't. Assuming the floor as a zero point, the change in potential energy is $mg\Delta{h}$, which is our answer, 2600J.

Finally,

But what's stopping me from saying the object has a constant velocity of zero which would mean the barbell would never move?

The fact that Lamar lifts the weight means it does not have a constant velocity of 0.