stat.useItem.minecraft.lead doesn't increase when a leash is used to leash an entity nor when the leash is used to form a knot on a fence.

it does however increase when clicked on a fence without a mob leashed. nothing will happen of course, but the score will still go up.

*To replicate*, create a scoreboard objective with the stat.useItem.minecraft.lead type and set it to the sidebar:

/scoreboard objectives add leash stat.useItem.minecraft.lead
/scoreboard objectives setdisplay sidebar leash

then try rightclicking with a leash...

• a mob and then a fencepost
• only a fencepost