The rivet holding the lace eyelet in place disintegrated:
A flat head 6-32 screw fit neatly inside the original grommet, making it flush on the side that matters and putting a stylin’ nyloc nut in full view.
When the only tool you have is a Basement Shop, pretty nearly everything looks like a project … and is fixable, too!
The Smell of Molten Projects in the Morning 
Nice. Has anyone ever accused you of being Scottish? ;-)
Verily, I am No True Scotsman!
I admit to an uncontrollable “I can fix that!” compulsion …