When I read that Yiddish phrase out loud, it sounded a lot like the English expression "to make a living". The English version is different than the Hebrew - it means to earn enough money to support oneself. And while all of the words are clearly English, to me it sounded like it could have been influenced by Yiddish, like the phrases "go figure" or "get lost". It has a real Yiddish ring to it, like in this joke:
Mr. Cohen falls and is laying in the road. A lady gets a pillow from her car and lays it under his head until the ambulance arrives.
"Are you comfortable?" she asks.
"Ah vell," he says "I make a living."
However, the phrase "make a living" in English predates Yiddish influence. The American Heritage Idioms Dictionary says it first appears in English in 1632, and the Online Etymology Dictionary has "living" in the sense of "action, process, or method of gaining one's livelihood" going back to 1400.
But I still think there might be a case made for a connection to makhn a lebn. Take a look at the Google Ngram Viewer for the phrases "make a living" and "making a living" from 1700 to 2000:
While there certainly are examples of early use, the phrases shoot up in the late 1800s and in the 20th century - precisely when the Yiddish influence on English began to grow dramatically.
Coincidence? You tell me! I have to go make a living, and if there's any free time - maybe also le'asot chayim...