Hello its good to see someone else interested in Lezhanivka genealogy. There is some records available through LDS, the village is grouped with the Bucyki records. The records are very fragmented and go from 1789-1865 with massive gaps, the death records are the most complete with 1789-1850 with no gaps.
With your family being from around early 1900's you will have same problem I am running into. The records from at least the 1880's through recent times are protected by privacy laws in Ukraine and to get copies of your families records, I just learned today, you need to provide legal documents proving your related. I have no idea how to prepare these documents are who and how to present them too once I do, this is very frustration since all i need are maybe one of the baptisms for my Elko Gudz or his brothers and sisters to determine who his grandparents are!
I hope you have a tad easier time about it then I have its like beating your head on a brick wall