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"Is it true that..." is a difficult question to answer. If you mean, according to a certain school, then yes, according to the Theravada, it is true, since an arahant is unable to practice non-monastic livelihood. They are said to either leave the household life or pass into parinibbana.
See, for example, the enlightenment of Khemā:
At the conclusion of the lesson Khemā was established in Arahatship; the multitude also profited by the lesson.
Said the Teacher to the king, “Great king, Khemā ought either to retire from the world or to pass into Nibbāna.” The king replied, “Reverend Sir, admit her to the Order; as for Nibbāna, never!” She retired from the world and became one of the Teacher’s foremost female lay disciples.
Dhp-A 347 (from Buddhist Legends)
N.B. the word "never" should actually be "enough!", in the sense that it's not time to think about that now.
The point is that, as mentioned in the linked answer, there is a difference between conventional morality and ultimate morality. Conventionally, only those livelihoods mentioned explicitly are wrong, just as only adultery is wrong for one who keeps five precepts. That doesn't mean that ordinary sexual desire is not ultimately misguided; it is. Likewise, any livelihood for the purpose of maintaining a household life is ultimately misguided.
The only exception I can think of is where one's household life is identical to a monastic setting (i.e. no need for ambition, concern for belongings, etc.).
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The quote was,
... most non-monastic livelihood is "wrong" in the sense that it generally involves desire beyond what is functional (i.e. can arise in an enlightened being)
I suspect that statement is related to Nekkhamma.
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Rosenberg, Larry, (2012), Breath by Breath. The Liberating Practice of Insight Meditation p. 124:
"Ordinary life is extremely important. After all, most of us are not monks or nuns in a monastery devoted to meditation. But if you take that [ordinary life] as a part of your practice—not inferior to monastic life and not superior—it can be extremely rich".
Isn't that what is really meant with catuparisa in the Sobhana sutra (AN. VII) , where the four groups [monks; nuns; lay man and lay women] are (...) 'accomplished together in wisdom, disciplined, self-confident, deeply learned and dhamma bearers, who live according to the dhamma and illuminate the sasana?'
Upvote:3
In Tibetan Buddhism there are many examples of yogis that didn´t live a monastic life but achieved enlighten during their lives.
The most revered of them is Milarepa, who after murdering family members in his early life, later became a Buddhist yogi and got enlighten.
Marpa is another good example; he had an ordinary life with wife, son, properties, etc. and got enlightened.
Milarepa and Marpa are both from the Kagyu school, but in all four schools of Tibetan Buddhism (Nyigma, Sakya, Kagyu and Gelupa) are examples of yogis, not living the monastic life and getting enlighten.