Aha, ok well disc brakes have a wearing in period before they reach full effectiveness so a noticeable improvement in performance would be expected after that sort of mileage. I'm not personally familiar with the Tektro model but I do use mechanical disc brakes, the Avid BB7s. Unlike hydraulics(or at least the better ones) they aren't self adjusting so setup and maintenance are more of a manual process. I followed these instruction for the BB7s:-
http://www.twowheelblogs.com/avid-bb7-disc-brake-set-and-tuning
Obviously the Tekros will differ but just reading that, and familiarising yourself with the sort of terminology, should help your understanding. It also depends on how much you want to do/learn yourself, nothing wrong with relying on your local bike shop. Basically mechanicals will rely on one pad moving and pushing/bending the rotor onto the other pad. The bite point and modulation will be influenced by where the rotor is within the caliper, ie central or more to one side or the other. You'll probably have adjustment at your levers and there is also the potential for loss within the cable system. As things wear you'll need to adjust the pads to compensate for this. Depending on the type of pad, organic/softish ones wear faster than metallic sintered, and type of riding/conditions will decide how often this needs to be done.
It all seems quite complicated at first but I'd say it's worth getting as familiar with these sorts of brakes as you would with a rim brake. I have seen some negative writeups around the Lyra brakes but without having messed around with a set myself I can't tell how much of that is down to setup issues. I do know of one potential problem where the brake releases when used hard, if you experience that then get them returned and swapped out. The BB7s are currently considered the best of the mechanical brakes(don't bother with BB5s) but if you swapped to hydraulics(I'm guessing not, due to drop bars) then the Shimano Deores get great reviews around price and reliability.