The Aklot lyre harps on the photos I've found on the net look to me to have 4mm size pins, but I can be wrong.
UPD: I think the simplest way to solve the problem is to buy a tap wrench set like this, one of them gotta fit your lyre unless the pins are too close to each other (unlikely). They work for tuning harps as well btw.
TIL people in general don't have calipers at home. My dad was an engineer :)