Disc brakes make a grinding sound I am completely new to cycling and purchased a road bike equipped with Tektro Lyra mechanical disc brakes. I have ridden an estimated 20 miles total so far and was unaware that there was a bedding in process for the brake system. My question is, how loud are the brakes supposed to be while in low to moderate use? My brakes have an slightly annoying grinding noise which sounds like metal on metal - no squealing, and they seem to shudder slightly when i pull hard on brake. I've tried reading articles and other questions to see if i can fix the issue however i am still a bit confused. 

If they were not bedded in properly is there something i can do instead of purchasing new pads and rotor?

Any suggestions on if this is normal during the break in period or if i should do something else to remedy the situation?
From your description there are two different areas this could fall under: problems with adjustment that are causing the rotor to hit the disc caliper or adaptor, or problems with bed-in. 

They shouldn't be loud under normal braking. You should get some slightly "textured" feedback as the pad bites down on the rotor as you use the brake, but it shouldn't shudder. That you mention shudder is the clue something is wrong here.

The first thing you should do is double check very carefully that the brake(s) in question are not adjusted such that the rotor can ever get contact the caliper body or the caliper adapter (if present). It should only ever be able to touch brake pad. If it's contacting anything else, hopefully it's just a case of re-adjustment, but too much riding like that can destroy things.

If that's not the problem, i.e. everything is adjusted properly but it's giving these symptoms anyway, the first thing I would do is remove, lightly sand, and re-install the pads, then lightly sand the rotor(s) and clean thoroughly with alcohol or brake cleaner. Then do a thorough bedding procedure after reading some good long thing that explains the theory and practice of bed-in. If they still do it, replace the pads. If they still do it after that, replace the rotor too. Some of the brakes out there now have this tendency to just start making a rapid-fire shudder when you brake, as the pad goes over the cut-outs of the rotor, and I don't know that it's even something that has to do with bed-in. Maybe.