My understanding is that "godly music" is music that, when played, flows along with the harmony of the natural world and is not jarring to it. I don't see it as particularly related to any particular lyrical content. In fact, I find that lyrics, particularly in one's own tongue, tend to engage the analytical side of the mind and is not conducive to flowing with the melodic content of the music.
Most modern music does not flow with the harmony of nature and so could be said to be ungodly in nature. Classical music, in contrast, does tend to flow with natural rhythms rather than representing a jarring interruption to it and could be said to be Godly.
A modern example of Godly music is that of Phillip Glass, whose album "Glassworks" contains music that flows beautifully with natural rhythms and when played in a natural settings will tend to heighten the feeling of divinity experienced and may receive a positive response from singing birds contributing to the music and the general atmosphere. I have experienced this myself when camping in a isolated spot and playing his track Opening, from Glassworks, and experiencing a real heightening of the divine atmosphere which swept up the bird song in the area and resulted in a crescendo of bliss!