For starters, most Lyme disease and CFIDS sufferers have problems detoxifying heavy metals and other toxic chemicals which are found in water from corroded pipes. There exists a well-founded rumor that Borrelia burgdoferi loves to sequester heavy metals and plenty of these, especially mercury and lead, can be found in most tap water systems. What's more, the enforcement of chemical levels in water by the EPA is inadequate.
Then there's the flouride and chlorine. Whoever decided that flouride was a great thing to put in toothpaste? Flouride is extremely damaging to the body as is chlorine. Both have been associated with increased incidences of certain types of cancers and other diseases.
Finally, tap water is aswim with critters--parasites, bacteria and other organisms that wreak havoc in the body. These exist in tap water, despite chlorine, which is added, paradoxically, to kill the buggers. Again, a person with an amazing immune system might be able to contain or kill the pathogens entering the body via tap water, but the immunocompromised Lymie might not be so lucky.
Using a good, quality carbon block or reverse osmosis filter can help eliminate toxins in water, and these are relatively inexpensive. For a couple hundred dollars, you can obtain a purifier which will save you from the perils of tap water, and in turn give your body an added boost to fight Lyme disease.
Oh yeah, and just one more thing. Forget about bottled water. Its quality is also loosely regulated and much of it isn't better than tap water. Besides, the plastic alone used to bottle water is toxic to the body. If you must carry water, you are better off using a glass bottle and filling it from home with filtered water.