In a Lorentzclock the light is bounced between the two mirrors with his speed of appr. 300.000km/s. Now when things speed up their time goes slower. But the light is always c, so in the Lorentsclock it also goes with c independent on the speed of the clock. But how is it possible that times slows down, but the light in your Lorentsclock doesn't/can't go slower while every bounce would be a second.
Perhaps this situation could be compared with light in a big gravity. But there the light is making a bigger distance due to curvature of spacetime. So the light still is c but looks going slower because the distance is bigger. Is that also the case with light if you travel with it?