All happy families resemble each other, each unhappy family is unhappy in its own way.
Famously from “Anna Karenina” and generally considered one of best first sentences of a novel ever.
I never thought I would see it in Italian but it sounds fine, too.
The “lo” has suprised me; I would have doubled the “infelice” or tried " … è cosi …".
The original Russian text repeats the word “unhappy” (Все счастливые семьи похожи друг на друга, каждая несчастливая семья несчастлива по-своему). In fact, the effect is much stronger. This translation you indicated seems to have made a questionable choice. I have a version of the text in Portuguese here, and it preserves the parallelism of the original work.
Flora, I believe that in this case, the pronoun “lo” simply replaces “infelice.” In that sense, it does not establish a direct relationship with “modo.”
It would be as if in English we wrote: “Every unhappy family is so in its own way,” where “so” stands in for “unhappy,” rather than agreeing with “way.”