One Lekic clan has its roots in northeastern Montenegro. They belong to Vasojevic tribe. All church records were destroyed over centuries (as indeed were the churches) by Turkish invaders, but the first use of the name can be traced to mid 19th century, to a person called Lek.
The second clan comes from central Montenegro and I am unaware the two are linked by blood lines.
In summary, Lekic family name comes from Montenegro (formerly a republic of Yugoslavia).