If I listen to a song and transcribe the lyrics myself, do I still require a license to put them up online and profit from them via ads on my site?

Missing the point.

Transcribing the lyrics yourself is kinda like writing the list of ingredients - it's a statement of fact. "The lyrics of this song are X."

Copying that effort from someone else, alternating apostrophes and all, is a bit different. In most cases, you can't prove that's what happened, but it's quite clear here.