FWIW I have been treated for early-stage Lyme twice, both times with amoxicillin, which is often a little gentler on the body than doxycycline (and you don't have to give up alcohol or sunlight). Fortunately it seems like Lyme isn't (yet) too picky about which antibiotics should be used to fight it.
probably, my wife had it, and she received doxycycline. She felt terrible for days, not fun. Fortunately we discovered the tick, and later the "bullseye" quite quick, so we hope that it exterminated everything.
There's a doctor in Hungary specialized on Lyme who treats it with doxycycline or amoxacycline and azithromycin.