Lyme is a terrible disease to have, but what value would it have as a weapon?
If you are a major world superpower, and you want to impede other powers from threatening you, but you want to avoid any kind of overt conflict, you might be interested in developing weapons that would slowly, over time, degrade a rival's ability to aspire towards greatness. Secrecy and plausible deniability would be most important, so something that is slow to take hold would be useful, since nobody would be able to trace it back to you. It doesn't even have to do anything in particular, it doesn't even have to target any specific thing. It just has to degrade their capabilities.
So if, for example, you had a weapon that you could deploy completely undetected, that would, over the course of 20 years, cause widespread low grade health problems which cause the target nation's expenditures on healthcare to rise by 3 percentage points of gdp... well that degrades their ability to spend that money on military or other threats to your hegemony.
That said, I think this particular conspiracy theory is stupid. What one of the above posters said is true: we have too much knowledge of the source and origin of Lyme for this particular one to be true. But, in general, I don't think that _a version_ of conspiracy theories like this are _laughably and obviously_ false
I also don't think the current iteration of the theory makes any sense for other reasons (especially the notion of creating a disease). But the idea of investing in germ and virus based biological warfare seems a very reasonable conspiracy theory, so I wonder to what extent the current Lyme disease is a modification of a more realistic one.
Kinda like the whole gay frogs rant some conspiracy theorist went on about that has become slightly famous. If you dig into the actual story, there were chemicals causing the frogs to undergo sex change. Turning gay seems a simplified version of this (especially to those not well informed on LGBT specifics). As such, while the actual conspiracy theory was wrong in the same way 'the earth is a sphere' is wrong, the knowledge wasn't that far off the mark.