It is definitely not true that most vaccines infect you with the virus. Most vaccines do not use live viruses at all, and the ones that do are specifically modified to be extremely weak.
This particular Lyme vaccine, VLA15, is a recombinant protein vaccine. IIUC it is basically just a particular protein that your immune system can learn to recognize and attack.
This is the nature of viruses..like it or not.
And live vaccines are often used because they tend to be more effective.
To be clear, I am only talking about live vaccines. Protein/mRNA vaccines give you antibodies without the virus, and I have no qualms with them.