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The phrase "lack of which" is correct and usable in written English.
You can use it when discussing or referring to something that was previously mentioned or described in the text, usually referring to something that is absent or missing. For example: "The old man was complaining of the hardships of living alone, a sense of community and companionship, lack of which can lead to loneliness and depression."
Exact(60)
There's iron, lack of which causes widespread anemia.
He has everything — except patience and consistency, the lack of which can be engaging, too, in its way.
Providing the poor with extra vitamin A (a lack of which can blind or even kill) is especially cost-effective.
Hypocretin-1 is a hypothalamic neuropeptide that is important in the regulation of wake and the lack of which results in the sleep disorder narcolepsy.
Swiss researchers have already used genetic engineering to develop a strain of rice with vitamin A, a lack of which now causes millions of cases of blindness.
But depression doesn't have to come automatically with a private office (assuming your organization has private offices, a lack of which might also be contributing to your depression).
It is is fitted with a gene that produces carotene, which in effect is vitamin A - lack of which causes blindness in tens of millions of children.
The result is an extension of concepts in neural systems towards phenomenal intentionality: the lack of which is a common starting point for critiques of AI.
Although he wore the appropriate coat and necktie -- lack of which is a well-known barrier to admission -- the problem was his pants.
It is the elevator, the lack of which had been noted at the Stuyvesant, that more than anything denotes the genteel quality of the Osborne.
But by channeling it back into the parties, it would reintroduce accountability to the system, the lack of which is what makes super PACs so pernicious.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com