source of Lyman Alpha in the Sun???
You are correct that Lyman Alpha is the n=2 to n=1 transition of the neutral hydrogen atom. One formation mechanism for Lyman Alpha is ionization and recombination. At the temperatures of the solar chromosphere, a substantial fraction of the hydrogen atoms have their electrons stripped away. Some of these electrons then recombine with hydrogen ions, and start to cascade down through the levels until they reach the ground level. However, even at 20,000 degrees, not all of the hydrogen atoms are ionized. This is because the density is so low that collisions are not frequent enough to knock off the electrons from all the atoms faster than they can recombine. Thus, there is always a population of neutral hydrogen, which also contributes to the Lyman Alpha line.