This is going to be difficult, and in the long run impossible, to express using existing patterns in English orthography.
That’s because if you mean for your word to end with the KIT vowel, then that is impossible under the rules of English phonotactics. That’s a checked (or lax) vowel and so cannot occur at the end of the word. Other checked vowels include those in TRAP, DRESS, STRUT, PUT.
So I’m pretty sure you want the FLEECE vowel, or if you distinguish them, the HAPPY vowel. That would be therefore not /ˈlɛvɪ/ but /ˈlɛvi/ or maybe /ˈlɛviː/ if you have phonemic length (Americans don’t).
As Peter Shor points out, we already have a word levy that is pronounced that way; likewise levee.
Even if you manage to get people to say some version which is like lev plus ick but without the ck, it will quickly fall back into the allowable patterns of English and end up being just levy (or levee) again to rhyme with bevvy (short for beverage) and Chevy (short for Chevrolet).