The word Lehre (f) in German, meaning an apprenticeship is a cognate to the English word Lore.
Looking at how the words are spelled, we can already see the similarities. When we take a look at their meaning however, it is not so obvious.
Let’s start with Lore.
Lore has the meaning of traditional knowledge and stories about a subject passed down among the members of a culture. An example would be:
The most famous creatures belonging to the Arabic lore are the Djinns.
This refers to the Djinns as part of Arabic stories and culture.
This meaning of lore gave us the word Folklore. Meaning the lore or traditional knowledge or stories of the people.
A second and most recent meaning for the word is the collective history and all knowledge about a fictitious universe. An example of this would be the following:
Dementors are a staple of the lore of Harry Potter.
The word lore here refers to the established world created by the creator of the Harry Potter universe.
The German word Lehre, on the other hand, has the meaning of apprenticeship.
Er hat seine Lehre als Mechaniker beendet.
(He has finished his apprenticeship as a mechanic.)
Lehre here refers to the amount of time the individual spent learning the profession.
That is not the only meaning for the word. It can also be used with the meaning of lesson or theory, even doctrine.
Das soll dir eine Lehre sein!
(That will teach you a lesson!)
Lesson refers to an experience from which an individual learns something.
We start to see a point of convergence here – all these uses for both words in English and in German have something to do with knowledge. And being more specific, they all convey a meaning of passing down knowledge or by extension, learning something.
If we go back in time, we’ll see that the word Lore comes from the Old English Lar, meaning learning, what is tought, the art of teaching.
In German we don’t have to go back in time, since Lehre actually derives from the word Lehren, currently still in use, which has the meaning of teaching, pass down knowledge.
Both Lore and Lehre evolved from the Proto-Germanic *laisti-, teaching, doctrine. And this word is believed to derive from the Proto-Indoeuropean root *lois-, which would have meant furrow, track. This makes these words cognates.