Pulleys do not inherently make a lift easier. They can make a lift easier, or they can simply be employed to change the direction of the load—such is the case with the lateral pull-down machine in the image, above.
(The machine in the image, in fact, has numerous pulleys, all but one of which change the direction of the load. The pulley at the bottom, just above the weight stack, functions to moderate force imbalances between the two arms.)
The weight of the stack is pulling downwards under gravity, but we want to be able to pull downwards against that weight, thus simulating a pull-up. That cannot work. So a cable is run over two pulleys—one above the weight stack and one above the lifter—to change the direction of the load. In an ideal (theoretical) machine, those forces would be identical. That is, if the weight on the stack were 490 Newtons (≡ 50 kilograms/110 lbs), so too would be the minimum force required to move that stack.
In the real world, however, friction resists movement in both directions. The stack is harder to lift, but easier to put down. This phenomenon may offer part of the explanation for its being easier than a pull-up: although the concentric phase of the lift requires slightly greater force, the eccentric phase, which fatigues us more, requires a slightly lesser one. However, the effect of friction is generally only appreciable on low-quality non-commercial machines; the friction on well-serviced, high-quality commercial machines is negligible.
There is most likely something else at play here.
The most likely reason is inaccuracies in the loads indicated on the stack. Loads are commonly exaggerated, even on machines of commercial quality. Indeed, whether by design or due to poor manufacturing tolerances, this is the standard. We should therefore accept the loads indicated with caution, and generally assume that they are only meaningful or trustworthy in relative terms—that is, compared with each other.
We can test the load simply by pinning the equivalent of our body weight to the stack, then hanging from the bar/handles. If the load indicated is precise, we will be supported in mid-air, perfectly counterbalanced by the weight stack.
Finally, as mentioned above, pulleys can be employed to reduce the effort relative to the load by some factor known as mechanical advantage. The benefits of this is twofold: the load can be graduated using the same weight plates, and importantly, twice the length of cable can be pulled without increasing the size of the machine. Cable pulley machines such as tricep push-down, functional trainers, and cable cross-overs are designed this way. But the lateral pull-down is generally not. (If your specific pull-down is designed this way, the stack will be lifted half the distance that the cable is pulled down.)
I hope that answers your question.