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Lithuania is definitely named in honor of Lithuania.
In general, I don't know. Is this a trick question? Does "country" specifically refer to a state? And does "named in honor of" necessarily mean that the name of one is contained within the name of the other? There's a chance that this "honor" was bestowed in some other way. Also, the country should be young or, at worst, the result of a revolution.
These aren't questions for the host; he's not obligated to answer them. Rather, these are just thoughts out loud.