Lit: a library for building fast, lightweight web components

I don't know if there is a particular benefit, it's just different. On the consumer side there is no difference, because they consume Web Components, and that is what both solutions deliver. On the implementation side, I can think of a few differences:

Vue is more of a "framework" solution and has more things built-in. You can do the same things with Lit, but the implementation would look different, because you'd lean more on native APIs. A good example of that is the event model, Vue has some event model built in, but with Lit you would use EventTarget.dispatchEvent().

Lit is a runtime solution, it doesn't require a build and you can load your source directly in the browser. Vue on the other hand requires some form of compiler stage to produce something your browser can use. Compilers these days are fast, and Lit is specifically engineered to not have runtime performance overhead, so in practice this difference is rather minor. It is a very fundamental difference, so I think it's worth pointing out.

Vue can compile to other targets. If you are only delivering Web Components, this is mostly irrelevant, but in theory a consumer might be able to use the Vue components directly in their Vue project, which might give them a better DX. On the other hand, Lit is specifically designed to produce Web Components, so you'll probably have a bit less friction compares to using Vue, e.g when some Vue concept doesn't compile cleanly to Web Components.

Is there a major benefit to choosing one implementation over the other? I don't think so, unless you have a very particular requirement that one of them addresses that the other doesn't. For nearly all cases, it is just a different implementation syntax.

In most cases the only relevant metric in deciding between them is what technology your developers are more familiar/comfortable with.