Lewis Carrol is actually really fun in just a pure markov chain; usually the diction is sufficient to put someone in the mood for Carrol, which means nobody really expects it to make sense anyways.
One of my favorite parts of Gödel, Escher, Bach was the description of translating Lewis Carroll's Jabberwocky into various languages -- particularly troublesome since the original poem contains few English words to begin with.
I think that just highlights how hard poetry is to translate in general. Carroll picked those words with thoughts to how they sound no less than other poets that restrict themselves to English words.
Translating poetry well where both meaning and sounds are vital can be harder than writing the poem in the first place was.