Do servo motor specifications take into account the gear ratio inside?
In general, for a motor with integrated gearbox, specifications in the data sheet are "at the shaft" which is the shaft that comes out of the gearbox.

In the case of hobby RC servos, like the one you're linking to, it is always the case that the torque takes into account the gear reduction (because it's a bigger number, thus better marketing.)

When you say "lift 4-5 lbs" you do not specify the distance of the lever arm. For a winch that winds a cable, that arm is the distance from center-of-horn to outermost-layer-of-cable. If you attach an arm, it's distance from center of servo horn to center of weight, projected to the ground plane.

You also don't specify how far you need to lift the load.

And you should know that most motors (and certainly all cheaper, hobby-style servos) are specified in maximum "stall" torque, which is not a level of performance they can provide on a continuous cycle. If you stall the motor for more than a few seconds, you are likely to burn it out. The "holding torque" or "continuous torque" is typically 0.3 to 0.15 times the stall torque, depending on motor construction, cooling, etc. This important data isn't even generally available for hobby servos, but is often specified for industrial automation components.

Also note that that servo likely has, at most, a 180 degree rotation angle.

A better Stack Exchange to ask this question on might be the Robotics Stack Exchange. I don't know how to go about moving questions/answers, though.