I guess they can, but the wild animals are the primary disease reservoir, mostly just because there aren't all that many ticks feeding on humans and making it back into the wild.

It also matters what species egg laying females feed on. The first few paragraphs of this lay it out:

http://wwwnc.cdc.gov/eid/article/16/3/09-0911_article

No the ticks get Lyme from the deer mouse, which is the reservoir species for the bacteria. After they feed on mice, they can give humans Lyme as nymphs or later as adults. http://www.tickencounter.org/tick_identification/deer_tick_l...