The Lyman series is brighter than the Balmer series. Why? Why was the Balmer series discovered first?
The brightness of the emission line (its intensity) depends on the number of photons emmited.
The number of photons emmited depends on the number of hydrogen atoms that end up in the final state (n=1 for Lyman and n=3 for Balmer).
The energy of an atom depends on its energetical state. The larger the n, the more excited the atom is - It has more energy.
Every system in nature (atoms included) tries to be at the lowest minimal energy possible.
Thus an atom that ends up with n=1 (Lyman) is ...
A detailed discussion of the Lyman and Balmer series.