Why are DNase and lysozyme in lysis steps used during protein purification?

If you are purifying a (often specific) protein, you will need to get rid of as much garbage as you can that might be bound to them.

It depends to an extent on which protein you are after, but generally it is a good idea, especially in preparative purification, to get rid of as many impurities as possible.

1:
As proteins are generally large, and consequentially will appear in the lower bands of your (ultracentrifuged) fraction, you want to get rid of any nucleid acids, especially if the protein you are puryfying concerns the likes of Pol1 , Reverse Transcriptase or any other enzyme involved in Replication/Transcription/Translation..

You can separate the Nucleic acids present in the sample by using a DNAse: this will totally hydrolyse DNA into its constituent parts.
Mind you, there are various DNAse's, all differing in their mechanism and specificity for their substrate. Depending on the DNAse used, it can show either Endo- or Exo- nuclease activity...

More to the point, RNAse is more suitable, as RNA is usually more within the buoyancy/fraction range of proteins, and can be bound to the protein.

2:
Lysozyme : An enzyme that has at least two functions:
It deglycosylates enzymes: Most proteins carried in the bloodstream are Glycosylated: they have a few sugar molecules attached to them. Lysozyme will remove the sugar-residues.

It also has the capacity to break down the cell wall of Gram-Positive bacteria, causing them to lyse . (if you want to purify protein from Gram-positive bacteria)

Any degraded products, either nucleic acid or sugar debris, will appear at the top fractions of the Centrifuge Tube due to their "lighter" buoyancy....