From time to time I see this word in print, though I have never heard it spoken. My guess it's a rarely used word which is not really used in speech that much. And the wiktionary does not show any pronunciation for this word.
I "feel" the stress should be on the second syllable, but how is the <ch> actually pronounced? As /k/? As /tʃ/? Some other way?
Your intuition about the stress going on the second-to-last syllable corresponds to the usual rule for stress in words ending in the suffix -ic. (I made a list of the exceptions to this rule here: Words pronounced with stress patterns like in “politics”, “lunatics”, etc.?)
I wouldn't recommend pronouncing the consonant corresponding to "ch" as /tʃ/ or /ʃ/, since those correspond poorly to the etymology from Polish/Slavic "Lech".
Surprisingly to me, the Oxford English dictionary gives the pronunciation as /lɛˈxɪtɪk/, with the /x/ sound, which is used by some English speakers in "loch" and "Bach" but is not a part of the general phonological inventory of most English speakers.
(Also, it says the etymology is from "German lechitisch", which as far as I know would actually be pronounced with the sound [ç], not [x]. But whatever.)
However, it is common for English speakers to replace this sound with /k/ when adapting words from foreign languages, so I would expect /lɛˈkɪtɪk/ to also be considered acceptable.
Many words in English are actually "borrowed" from other languages. If the word is transliterated from a different alphabet (like Polish), the English spelling is meant to approximate the pronunciation in the original language, but the actual pronunciation is meant to be as close as an English speaker can manage to the original.
There are hundreds of such words — for example, the sauce catsup/ketchup is from the Chinese 茄汁, pronounced more like "ke-jap". Over time (sometimes very quickly) the pronunciation is anglicized to something native speakers can easily pronounce. Another example, karaoke, is borrowed from the Japanese, who pronounce it as "kah- rah- oh- keh", while many Americans pronounce it more like "carree- okee".
(As a side note, the "oke" in "karaoke" is actually an abbreviation of the English word "orchestra", which the Japanese themselves borrowed. It goes around and around.)
Lechitic itself comes from Polish:
The term Lechitic derives from the most popular form of the name of the legendary forefather of Poland, Lech (apparently a distorted form of *lęch). Furthermore, Lechites (Polish: Lechici) was an ethnic and linguistic group of West Slavs, the ancestors of modern Poles and the historical Pomeranians and Polabians. source
I think the proper pronunciation of "lech" would be as close to the original Polish as possible, with the "itic" pronounced the same as in "Semitic" or "Levitic". If this video of (what I assume is) a native Polish speaker pronouncing "Lech Walesa" is accurate, "Lech" is pronounced with a "hard" ch sound, like chemist or chorus. Therefore Lechitic is likely pronounced as "lek- i- itic" — with some possible, subtle variations.
