For what it’s worth, in 2022 with OmniGraffle Pro 7.19.5 I’m also having trouble with this. I see the drop-down with “Follows Path”, “Parallel”, etc. but I can not figure out how to get it to become enabled. I’ve tried selecting the line, selecting the label, and selecting the text of the label. The first isn’t expected to work and I think it’s dubious whether the last one should work (but rwx makes specific mention of this, above). I think selecting the label itself should work. Regardless, none of these enables the drop-down for me.
Hmmm… in a new document selecting the label or the text or both enable that drop-down. So what’s the difference between that new document and the one where I actually need to do this? I’d say that there’s a bug here someplace.
If I cut and paste the line with the parallel label from the new document to my existing document, it maintains the label in the parallel position, but selecting that label still does not enable the drop-down menu.