Lysis step during DNA purification
You want to isolate the cfDNA, and leave anything else in the plasma out of your analysis — essentially, the lysis step is part of the purification.
(See here)
(I'll elaborate with edits shortly)
Edit:
Actually, it looks like lysis is not a good idea in cfDNA isolation — lysing cells in your sample will result in contamination by genomic DNA, as discussed here. It would be better to stabilize/fix cells to prevent them from lysing, to avoid this risk.
In other words, your initial instincts were correct!