Since the COVID vaccines don't seem to really prevent transmission or infection, I think the same is true for those.
Vaccines do reduce transmission, via (a) reducing the chance of becoming infected in the first place and (b) reducing the average duration of the infectious period. As far as anyone can tell, this holds up for omicron, at least for boosted individuals, though it's certainly less effective at preventing infection.
Some Covid vaccines reduce transmission. And it keeps you out of the hospital, which for a human-to-human transmissible disease like Covid (and unlike Lyme’s), is a big deal.
Unless they create a coordinated campaign to oppose an already approved Lyme vaccine to such a degree that the manufacturers think it's too much of a risk to leave it on the market.
In case others think you’ve stated a hypothetical, let’s be clear that this already happened.
But they might require hospitalization or other medical treatment, increasing the strain on the healthcare system resulting in worse outcomes for others.