This is not so much a question of vocabulary itself, but one of idiomatic use. In this case, for no reason that I can justify, we say "lack". Logically, however, any, except shortage , could be used correctly.
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CliveA, loss I had privacy, but now I don't have it.B, absence There is noneC, shortage There is some, but not enough.D, lack There is none, but there should be some.Great explanation!