I am trying to adjust the brakes of a new bike and need some help. It has mechanical disk brakes. I have successfully aligned the disk pads so that they are parallel and are at an adequate distance from the disk. However, the lever travel is ridiculous, it goes down all the way to the grip. I understand that in order to decrease lever travel you have to bring the pads closer to each other, however I have brought them as close as they can be already without causing brake rubbing. Any ideas on what I can do?
First I would determine for certain that the levers are compatible with the disc brakes. They should be long-pull levers and will be compatible with linear pull (V-brakes) rim brakes. Being a new bike, I would think this should not be a problem if sold by a bike shop.
Next, I would check that you have proper cable tension. You may have to remove all slack from the cable by loosening the pinch bolt and pulling more cable past the bolt, effectively tightening the cable. Also of use would be turning out the lever's barrell adjuster (anti clockwise) which also tightens the cable. This is the rounded end of the lever where the cable exits the lever. On brake barrell adjusters there are two threaded parts that move. The smaller one closest to the lever is a lock ring. When you've set cable tension appropriately with the longer cylinder shaped adjuster, you set this in place by turning the round part tight to the lever. To make any adjustments after this you'll first need to loosen the lock ring. Essentially, determine if any slack exists in the cable and correct this.
The lever travel is typically set with a small set screw found on the inside (toward rider) of the lever body, the part of the whole lever assembly that doesn't move. Tightening (clockwise) this screw shortens the travel. This maneuver, however, won't really help your problem since you experience inadequate braking to begin with. The lever travel screw works essentially by pushing the lever toward the handlebar, and is the same as the first few millimeters of lever closure your fingers do now. Shortening the travel won't help. Lengthening the travel by loosening the set screw initially puts slack into the system so without further cable adjustment, you're pulling the same amount of cable and therefore braking is unchanged.
Most mechanical disc brakes have separate pad and cable adjustments.
You want to set up the cable adjustment first. Hold the lever on the caliper at its fully retracted position, then pull the cable tight and secure with the pinch bolt. Use the barrel adjuster to fine tune slack out of the cable only, not to adjust the pad position. You want the caliper lever to move as soon as you pull the brake lever and the for it to have its full range of motion available.
Then, use the pad adjustment to set the pad separation from the disc.
Park Tool has a good page on mechanical disc brake setup https://www.parktool.com/blog/repair-help/mechanical-disc-brake-alignment.