Of course, the point of CSS is that sites that use it degrade in older browsers anyway, remaining legible even if the browser isn't supporting the whole CSS thing.
Of course, some browsers have buggy implementations of CSS, which is why so many CSS sites have to devote space to "CSS hacks" that rely on bugs in various browsers and versions of browsers to get them to ignore bits or interpret bits differently.
And even if a browser claims to support a certain version of CSS (most don't bother - IE doesn't, nor does Mozilla, and that pretty much covers the field 🙂) there's a chance it doesn't.
And, as hinted at, browsers don't usually say anything about what level of CSS they support or how much of it. And if the browser doesn't say, the server's not going to know.
laserlight's suggestion is about the best you can do. You could google around and find a table that lists client types and which CSS features they support, but I don't think the end result will really be worth the hassle.
Pages that use decently-written CSS2 or even CSS3 should look fine in Lynx without taking any of the CSS out.