If so, then shouldn't lightning be reflected back into the sky everytime it hits the earth, due to an impedance change?
It would be reflected back (almost) completely if the earth was metal but it is not. In fact the earth and sea present a dissipative load to the current pulse and there is also a fair amount sideways radiation that propagates very well in the cavity resonator formed by the ionosphere and the earth. It can and does propagate all around the earth and these lightning strikes are the main cause of interference into long range LF radio communications limiting not only their practical range but also any achievable information rate.
Note too that the cloud to earth distance is quite short relative to the effective wavelength of lightning (a 1msec pulse would have an effective wavelength on the order of ~300km), so there is probably not much to be gained by looking at it as a vertical transmission line whose length is ~10km. That is not the case for the EM cavity whose diameter 40,000km.