If my baby has a round, red, circular rash, could he have Lyme disease?

Unlikely. To develop lyme disease, you have to be exposed to a tick bite. Infants are unlikely to get bitten by ticks.
If you child or teen has had a tick bite, or been in an area where a tick bite is possible, consider lyme disease a possibility. The red rash looks like a large target. Test results can be falsely positive or falsely negative. If a tick has been removed, it is best to go ahead and treat.
Unlikely. Untill an infant is up walking around and getting into mischif, I doubt they would be exposed to the tic vector. I believe it must attach and feed for 24 hr before it will pass its germ. Most parents would notice a tic during bathing. That said, I have seen it in a 15 mo. The primary bite wound and secondary target ring lesion were dramatic. In infants a ring worm would be more likely.
Possibly. The classic rash of lyme looks has a red center, then a normal area surrounded by a red ring. Ticks are the most likely vector of lyme, but there is strong evidence that biting flies like deerflies and horseflies can transmit lyme (see http://www. Nejm. Org/doi/full/10.1056/nejm199006143222415) and it is theorized other biting insects may also transmit it. But there are many other causes of rashes.