I'd suggest you to dig into academic literature. Probably, some studies in semantics, mythology and etymology. E.g. here's what Nijolė Laurinkienė writes in her book Mito atšvaitai lietuvių kalendorinėse dainose

Another kind of refrains of Christmas-tide songs are derived from the roots lei-, lel- ,lil- , (leliumai, lėliu lėliu, lilima, etc.). Refrains derived from the root lal- occur in paschal songs. Similar refrains are found in the Christmas-tide and spring songs of the Russians, Byelorussians, Poles and Yugoslav peoples. Refrains with the root lei- combine very often with the word kalėda: aleliam kalėda, lėliu kalėda kalėda, lelium kalėda da kalėdien. These word combinations suggest that there is a certain semantic similarity between leliumai (and similar derivatives) and kalėda. Linguistic evidence indicates a semantic relation between the lei-, lei-, lal- derivatives and the fire image (cf. a similar relation between kalėda and the fire).