Why is the pH actually changing between lysis and washing...

When pH > pI, a protein has a net negative charge. When pH < pI, a protein has a net positive charge.

In the higher pH of lysis buffer(8.0), your His-tagged protein binds to the Nickle beads strongly, but at the same time some nonspecific proteins are negatively charged and bind to the Nickle beads.

In the lower pH of washing buffer (6.8), your His-tagged protein still remain on the beads with strong affinity due to its His tag. The nonspecific proteins bound to the beads have less (if not zero) negative charges and dissociate from Nickle beads. So after washing step, the nickle beads should only bind to the His-tagged protein.