You know well - no two words ever have the same meaning. If they do, one becomes obsolete or they are used in different styles or registers. Or they still mean exactly the same but are regional. Or if one of their meanings coincide, then one of them must have some added meaning, which the other one doesn't. And so on...
As regards your question, to us
ludicrous is more like charicature, farcical, besides being laughable and absurd
ridiculous is funny because of being silly and pathetic
But yes, they are very close in meaning and people's views will vary as to their exact meaning, I expect.
But certainly not the same.
PS. I've been thinking about your two words. Somehow, ludicrous sounds a bit more "serious" than ridiculous. If something is ridiculous, it is not so important, sort of. While ludicrous may be a bit more absurd, enough so to even scare you perhaps...