The one thing somewhat like the quote that he wrote, in 1914, was:
A new form of family, new conditions in the status of women and in the upbringing of the younger generation are prepared by the highest forms of present-day capitalism: the labor of women and children and the break-up of the patriarchal family by capitalism inevitably assume the most ...
It is almost an exact quote from Lenin's time, but not by Lenin.
Instead, in 1918, Sir John Robertson, the Medical Officer
of Health for Birmingham, UK said:
To destroy the family is to destroy the nation