Lyrics could mention Christ’s name and actual be quite opposed to what Christ was about. I could sing a song about how Jesus loves me more than he loves people outside the church, and (be using his name very much in vain.) These would, in some sense, be Christian lyrics. But they wouldn’t be lyrics that Christ lives in.
On the other hand, there could be words that don’t mention Christ’s name, even written by someone who does not profess Christ’s name as lord, that Jesus very much does live in.

This leads me to wonder, if that isn’t the real distinction, the real question for lots more stuff: we think what counts is whether or not we used Jesus’ name, but the real issue is whether or not Jesus spirit could inhabit what we do, think, and use.

A Christian cofee house uses Jesus name… It’s entirely a different question whether Jesus is actually present there. Ditto retreats, stores, all those other things. The label “Christian” is quite irrelevant in deciding if Jesus is really present.