Jocular and/or euphemistic way of referring to suicide.
Bob: Phil, have you seen Pete since he blew that interview?
Phil: No, but I heard he took it so hard he stormed off to the nearest bridge and went on his merry way.
Bob: LOL! Wish I could have been there to see it. Would have been the YouTube video of the century.
Pete killed himself. That is what it means to go on one's merry way.