… his mother was possessed of a tyrannical nature and led her peasants and also her immediate family a miserable life.
In idiomatic Present Day English, lead (past led) is not a ditransitive verb, i.e., one which takes two objects, like elected her president or gave me a lecture.
Curiously enough, this has not always been the case:
… if he behave himself well; but, if otherwise, they lead him a Life (as they say) like a Dog.— Roger North, The Life of the Honourable Sir Dudley North, 1744.
But Nabokov’s lectures were published in 1981.
What is missing is a causative — the tyrannical mother caused them to lead a miserable life – or a resultative — the mother made their lives miserable.
The easiest way to edit the clause would be to add a dependent infinitive:
… his mother was possessed of a tyrannical nature and led her peasants and also her immediate family to suffer a miserable life.
I wonder whether something like this was somehow omitted.
I could not readily find any details about Nabokov’s role in the publication of this book beyond his having given the lectures himself at various American universities. A New York Times review at the time of publication notes:
Fredson Bowers, who edited both volumes, says Nabokov's lectures were mainly handwritten. Sometimes they lacked clear organization, and parts remained in rough notes.
Whatever the case, a proofreader at the publishing house certainly should have caught the error.