My tied-on wrist straps have seemed low. They hold the instrument to my hand well enough, but I can't relax my arm into them and still reach the strings. I recall that at least one of the extant lyres has mounts for a strap, and they're higher on the arms. My knots won't hold up high, though.
Solution: Add friction! Photo essay below the cut.
That's a scrap of leather wrapped around the arm of the lyre, with the band tied tight, using two half-hitches, over it.
This is how I rest my arm in it:
Hand approaches instrument from rear.
Duck your hand under the strap and let it rest on the back of your wrist.
Twist your hand sideways. You're going to duck under the strand of the band to the side you're twisted towards, to put the twist behind your hand instead of in front of it.
Now your hand is dangling securely from your lyre, with the strap behind it pressing it forward into the strings for block-and-strum playing (or plucking, if you're more dextrous than I am).
How it looks from the front.
I still have to play with it for a few days to see how the technique holds up; if it ends up slipping every 30 minutes of playing time, then it's not so good. But it seems sturdy so far.