The ticks carrying the Lyme disease bacteria were trapped in the Northeast (for the USA). Climate change changed the feeding behavior of the prey of juvenile nymph ticks, the main vector for increasing the habitat is mice not deer. The adults feed on deer but most infections in people that we know about come from nymphs ( probably because they are so tiny).

A laymen's explanation:

https://qz.com/441583/lyme-disease-is-spreading-faster-than-...

"But our rapidly changing climate also seems to be making it easier for Lyme to spread, by shifting when blacklegged ticks typically feed."

This means it's simply a matter of waiting for the temperature to rise just a bit more for the Lyme disease to be a problem in the USA everywhere there are deer.

There is the difficulty with temperature theory helping the spread the same way in Europe which the article covers, but Lyme disease in Europe is a slightly different bacteria as well.

The National Science Foundation explanation: https://www.nsf.gov/news/special_reports/ecoinf/lyme.jsp