I've always preferred saying that I have an infection of Borrelia burgdorferi (Bb) to saying that I have Lyme disease. The latter term implies that Lyme disease is the cause of my symptoms, when I don't think we can say that with any certaintly.
It's always puzzled me that LLMDs, in particular, will see a person who has multiple infections, some of them tick-borne like Bb, and label him or her as having Lyme disease. How do we know that the Bb is the most important infection? What if that person also has HHV-6, EBV, Bartonella and Babesia? One of those infections may be more important. Or what if it's not the infections themselves that are the main problem, but a weakened immune system due to genetic predisposition, toxicity, methylation blockage or something else? What about people who test positive for Bb but are asymptomatic? Have they ever been studied?
Personally, I think that one can be infected with Bb and also have CFS (whatever that is). It doesn't seem right to me that having Lyme disease is an exclusionary criterion for Fukuda-based CFS. The problem with the Fukuda definition (like all CFS definitions) is that it doesn't depend on objective biomarkers. Down the road, when scientists have broken down the broad construct "CFS" into subsets that correspond to biomarkers, I bet plenty of people with the various biomarkers will also have Bb infections.
We already see this happening with XMRV. I know of at least three people who test positive for both Bb and XMRV. Assuming XMRV does turn out to be a biomarker associated with a subset of CFS (XAND), then yes--you can have both CFS and Lyme!