Diet only matter here in terms of supporting your immune response well whatever is not inhibited by a parasite. "Good diet" also = less inflammation = more resources sent to the battlefield, swifter response, etc.
However any diet will not change anything in terms of cure such as starving parasites which is a myth. Host will suffer here first before any parasite.
You need to consume sufficient amount of protein anyway during such infection for repair process (damage to the tissues, etc).