Ο Λουκάς Βαγιάς γεννήθηκε στο χωριό [[Λεκάλ]] στην περιοχή Λουντζάρι, στο τότε [[Πασαλίκι των Ιωαννίνων|Πασαλίκι των Ιωαννίω]], στην [[Οθωμανική Αυτοκρατορία]], σήμερα [[Επαρχία Τεπελενίου]], [[Αλβανία]].<ref name="Muci">{{Citation|title=Lekëljotët në Pashallëkun e Janinës|trans_title=Lekliotes in the Pashalik of Yanina|language=Albanian|publisher="Odria" Newspaper|volume=54|last=Miltiadh Muçi|date=April 2010|quote=Two of the four brothers Vaja have served with dedication, as friends and activists of Ali Pasha. All were educated in colleges and universities all over Europe, but most particularly was Luke, Kristaq and Jani as well.|url=http://odriegolik.itgo.com/index_6.html|access-date=2013-09-24}}</ref> Ήταν ο μικρότερος αδερφός του [[Θανάσης Βάγιας|Θανάση Βαγιά]], στρατιωτικού αρχηγού του Αλή Πασά. Είχαν δύο ακόμη αδέλφια, τον Γιάννη και τον Χριστάκη. Σύμφωνα με ορισμένες πηγές, οι ίντριγκες του Λουκά (και του Θανάση) ήταν ο κύριος μοχλός για τον [[Βαντζέλ Μέξι|Βαντζέλ Μέκσι]] να εγκαταλείψει την αυλή του Αλί Πασά και να διαφύγει στην [[Κέρκυρα]].<ref name="Lloshi">{{Citation|url=http://mapo.al/2013/08/24/xhevat-lloshi-zbulon-dokumente-te-reja-per-botimin-e-pare-te-dhiates-se-re-ne-shqip/|publisher=MAPO Online|access-date=2013-09-24|language=Albanian|last=Aida Tuci|title=Xhevat Lloshi zbulon dokumente të reja për botimin e parë të Dhiatës së Re në shqip|trans_title=Xhevat Lloshi reveals new documents for the first edition of the New Testament in Albanian|date=2013-08-24|quote=...Luka Vaja ishte dhe ai mjek i Aliut...'''[Luka Vaja was a physician to Ali...]'''|archiveurl=https://web.archive.org/web/20130927135914/http://mapo.al/2013/08/24/xhevat-lloshi-zbulon-dokumente-te-reja-per-botimin-e-pare-te-dhiates-se-re-ne-shqip/|archivedate=2013-09-27}}<cite class="citation cs2" data-ve-ignore="true" id="CITEREFAida_Tuci2013">Aida Tuci (2013-08-24), [https://web.archive.org/web/20130927135914/http://mapo.al/2013/08/24/xhevat-lloshi-zbulon-dokumente-te-reja-per-botimin-e-pare-te-dhiates-se-re-ne-shqip/ ''Xhevat Lloshi zbulon dokumente të reja për botimin e parë të Dhiatës së Re në shqip''] [''Xhevat Lloshi reveals new documents for the first edition of the New Testament in Albanian''] (in Albanian), MAPO Online, archived from [http://mapo.al/2013/08/24/xhevat-lloshi-zbulon-dokumente-te-reja-per-botimin-e-pare-te-dhiates-se-re-ne-shqip/ the original] on 2013-09-27<span class="reference-accessdate">, retrieved <span class="nowrap">2013-09-24</span></span>, <q>...Luka Vaja ishte dhe ai mjek i Aliut...'''[Luka Vaja was a physician to Ali...]'''</q></cite><span data-ve-ignore="true"> </span><span class="cs1-maint citation-comment" data-ve-ignore="true">CS1 maint: discouraged parameter ([[:Κατηγορία: CS1 maint: αποθαρρυμένη παράμετρος|link]])</span>
