Has the Lyman-alpha forest ever been used to test Halton Arp's theory that quasars are not cosmological but instead are ejected from relatively near-by galaxies? If Arp was right, then the spectra of the quasar and the 'parent galaxy' should both show the same Lyman-alpha forest; if it only appears in the quasar spectra, then the quasar must be much further away.
All possible tests of the Arp model have been failed. High redshift quasars have Lyman alpha forests, low redshift galaxies do not.
The Arp model suggests that the Lyman alpha forests are somehow intrinsic to the quasar. There are many problems with this idea.