Hello, I'm sorry to hear about Lucy being sore on the side that she was given her second Lyme vaccine.
It isn't uncommon for dogs to run a low grade fever and feel achey for 48 to 72 hours after a vaccine. It means that her body is responding to the vaccine and mounting an immune protective response.
You can use Benadryl (diphenyhydramine) at a dose of 1mg to 2mg per pound orally every 8 hours to help her feel a bit better.
If you know where the vaccine was given you can apply a cold compress 2-3 times a day for the first 48 hours, and then warm compresses for the next few days to ease discomfort.
And I'd call your vet in and ask for a short course of a nonsteroidal anti-inflammatory like Metacam, Rimadyl or Deramaxx. Those will really help relieve the aches.
Not all dogs respond this way but plenty do. Certain vaccines (Rabies vaccine and Lyme are two of the most common ones) are more likely to create this type of response. I wouldn't not vaccinate her because of it but I would use medications to relieve her discomfort in the future.
If she begins vomiting or has diarrhea, has any difficulty breathing or facial swelling it is time to have her seen on an emergency basis for a steroid injection.
Even if you choose not to ask for an anti-inflammatory prescription you should report this reaction to her veterinarian. It should be noted on her permanent record and the manufacturer should be informed.
In the future they may wish to pretreat her with anti-histamines or steroids when she is vaccinated as a precaution to prevent such reactions and/or send her home with some anti-inflammatory medications.
Please let me know if you have any further questions.