Apparently, there were numerous noble Lázár and Lazár families (the diacritics above the "a" letters are very important in Hungary, making these essentially different vocals from the ones writeen without the accent). One Lázár family were even counts.

You may want to search at http://www.arcanum.hu/gesta/ but you need a Hungarian speaker to interpret what you'll find there. My own Hungarian is unfortunately limited to some guessing.

Debrecen was a large city, with multiple parishes of several religions. LDS has films of the records, but you might be in for a long search. Nevertheless, unless you hit luck, you must first establish your own line if you want to have any chance to connect to any of the noble lines.