I am an utrarunner and I also have Lyme.
I have been running longer than I have had Lyme, as I believe my first bite was in the early 90's...and that is when I was infected originally. I have been running off and on(more on than off)ever since. I will say as others have, that listening to your body is key. I will disagree with the fact that you are over stressing you system. I truly believe the fact that I am a runner is what has helped me to not get sicker than I did. I have had to take time off when I have been too sick to function, neer mind run, but as soon as I felt better, I added back the running and do believe it aided in my recovery.
My most recent treatment was 6mo of abx, plus herbal *stuff*end of last year/early this year, then I started low dose Naltrexone(which I believe totally saved me)Since I stopped the abx in March(I think) I have been running regularly, 50-70 miles a week and completed 3 races of 50+ miles.
All that to say don't give up the running! If you run by how you feel, eat a really good diet and stay hydrated, I would say youy will probably be able to run more than not run. ESPECIALLY since you caught it early. I didn't get adequate treatment until I had been dealing for 13 years, then a Dr finally figured out what was going on.