I find the cisarik.com site to be really helpful for quickly figuring out the corresponding current Slovak village/town names for what were previously recorded with their Hungarian names... and then determining where to look for records according to which religion someone practiced.
For example, for Michael Lesnansky, if he was Calvinist/Reformed Christian let's say, and from Falkus/Falkušovce, then I'd find the village name on the Cisarik site and click on it. On the left column it contains a summary of the various religions that may have been practiced by residents of the village in the past and where the corresponding church records were kept. So for Falkušovce, the "ref" is for Reformed Christian I believe, so you'd want to check the records for Málcza, which is of course the old Hungarian name. So go back to the list of villages, looking under M, click on Málcza and you'll see it loads the page for Malčice, what the village is known as today in Slovakia.
So then to browse the correct church records in image form on FamilySearch for a possible baptism record, you would select Slovakia Church and Synagogue Books, 1592-1935 > Reformed Christian (Reformovaná kresťanská cirkev) > Michalovce > Malčice and then the correct record "book" (there's only one in this case--the name just got split into 3 columns from what I can see).
Unfortunately, if my assumption that he was Reformed Christian and baptized in Falkus was correct, it seems the baptism records are not available after 1895 for the Malčice Reformed church (and you need to see 1897... so close!). That said, there are certainly Lesnansky variant names in that last book in that time frame, which is encouraging. Like a baptism on 1895-08-22 for Zsuzsánna Lyesnyánski, daughter of János Lyesnyánski and Zsuzsánna Adám (I think), from Falkus. So possibly a sister? Maybe a cousin? That's on page 239: https://familysearch.org/ark:/61903/3:1:S3HY-6G29-Q?cc=1554443&wc=9PQD-FMH%3A107653801%2C110350301%2C111028201%2C1160768906