Lilt, “a rhythmic swing or cadence; a light and merry song or song or tune,” comes from Middle English lilten or lulten (14th century), meaning "to sound an alarm" or "lift up (one's voice"), possibly related to Dutch/German lullen ("to lull") and Norwegian lilla ("to sing"), suggesting an imitative origin for its musical, rhythmic sense of a light, cheerful tune or speech cadence, likely stemming from onomatopoeia.  It entered English in the 14th century, with the "singing" sense emerging later (18th century).  

According to the Oxford English Dictionary (OED), the first uses of "lilt" in English depend on whether it is used as a noun or a verb. 
As a verb, the earliest known use of "lilt" is from around 1400 in the poem Pearl. The original meaning was "to lift up (one's voice)" or "to sound an alarm".  As a noun, the earliest known use is from 1728, found in the writings of the Scottish poet Allan Ramsay. The initial noun sense was for a "lilting song" or a rhythmic cadence.  Other related forms also appeared in the Middle English period, such as "lilting-horn" (around 1384). 

Examples of "lilt" in a sentence: 
"There was a charming lilt to her voice." 
"it's a tune with a catchy lilt" 
"A gentle lilt greeted me and offered to help."
"His voice has a jazzy lilt and the swagger of that era." 
"Just listen to the meter of his lilt, the melody of it." 
"And Adam Cork's music is full of the blarney of Celtic lilt." 
"It has a lilt, like gentle waves washing ashore."