Lyme disease can cause twitching. There are certain common symptoms that many people who have lyme disease get, but they're all subjective to each individual. If the twitching is interfering with your activities of daily living, you should consult immediate attention from your physician so it can be monitored.
Yes, twitching is said to be a cause from having Lyme Disease. You should consult your physician to see if there is any medication that you cant take to help.
You need to go back to your doctor. Yes, Lyme disease can cause neurological problems if not treated quickly enough. I hope that you have received proper treatment by now.