I was diagnosed with and treated for Lyme a few years ago.

At the time, my physician mentioned that a previous infection would provide "a limited immunity" (exact quote).

Since then, I've had two bulls-eyes but no symptoms (oblig anecdata).

It appears that you develop an immunity only to particular strains of the bug:

http://iai.asm.org/content/early/2014/01/07/IAI.01451-13

They drill into crevices in muscle tissue and are able to avoid the lymphocytes. It's hard to effectively become immune.