*leis-, *lois-

The core idea of this root was:

track, furrow

From there, it shifted toward the broader sense of pursuit and eventually even further toward pursuit of knowledge.

Here’s a quick overview over English family members:

• to learn (pursue a trace to knowledge)
• lore (what is learned)
• to last (follow a track, stay on track -> remain)
• delirious (Originally “off track->crazy” in Latin)

The meaning of German leisten evolved from a sense of following directions, doing your work and then shifted a bit toward getting results.