*lŭg-

The core idea of this root was:

bending

According to the German source I am using (DWDS.de), this is the origin of leek and garlic and the lock in the sense of curled hair.

The German etymological dictionary also mentions that through the idea of bending a branch into a hook, this later extended into the sense of closing of the Germanic root *lukana, which is the origin of the English to lock and the German das Loch (the hole).

It’s the oirgin