There is a clinic in London called London Clinic of Nutrition, they treat lyme, they are naturopaths and treat with herbs only (not doctors), it is possible to have an appointment over skype, I am not sure about
the first appointment but you can contact them, probably they're
open to all options. For the blood work, they use ArminLabs in Augsburg, you go to the clinic for the blood draw, and they send it to Germany. Perhaps you could go directly to the lab, after they tell you what to test for.
There is also a lyme specialist (also naturopath) that used to work at London Clinic of Nutrition (I am not sure if she still does), but I see she started her own clinic http://arthealthclinic.co.uk/ She also has great reviews.
Breakspear Medical treat lyme disease, these are medical doctors.
There is IHF Clinic where you could get IV antibiotic infusions at a decent price - so they say, haven't tried it. (also London)
Dr Kenny de Meirleir is famous for treating lyme in Belgium.
There is a clinic in Cyprus that treats lyme with ozone, and I read online some people had success. - dr Nikolenko, ycmedinstitute.com and neomedinstitute.com
I also found two german websites treating lyme http://www.bca-clinic.de/ and http://www.dr-hopf-seidel.de/borreliose-symptome-1.html - I don't speak a word of german, don't understand any of this
There is a doctor in Trieste (Italy), prof Giusto Trevisan, I think he is the only lyme literate doctor in Italy.
I apologize if I shouldn't have written the names, please delete the post. Most of these doctors/therapists either advertize publicly anyway, or are very well known, and I guess the situation is a bit better in Europe with regards to letting people treat lyme - but there certainly is much less LLMDs than in US.