In Joel 2:31 NIV, which says that
The sun will be turned to darkness and the moon to blood before the coming of the great and awesome day of the LORD.
as well as in Mark 13:24-25 NIV
However, after the tribulation of those days, ‘The sun will be darkened, and the moon will not give its light, the stars will fall from the sky, and the powers of the heavens will be shaken.’
These verses contain the most probable meaning of the verses, especially considering the different fourth line on this website. Seeing that the last line in that version is "King Jesus will be mine", the lines most directly refer to the coming of the Son of Man and the events preceding it. So the second and third lines do not allude to the death of Christ, but rather, the second coming of Christ.
As for the 1st line, "The moon runs down in a purple stream", it refers to two things. First would be the "purple" color referencing the royalty of "Jesus" in the version above. Second would be the "runs down" refers to the moon turning to blood in Joel 2:31, afterward not giving its light as in Mark:13:24-25.