They really don’t.
1. The lie in question.
Beauvoir didn’t provide insight of her own here, it’s a paraphrase of certain arguments from Fantasia of the Unconscious by D. H. Lawrence:
Better Anna Karenin and Vronsky a thousand times than Natasha and that
porpoise of a Pierre. This pretty, slightly sordid couple tried so
hard to kid themselves that the porpoise Pierre was puffing with great
purpose.
That doesn’t mean that having great purpose is bad, it’s just Pierre’s life project seems fake to Lawrence.
no man ever had a wife unless he served a great predominant purpose.
[…] Only I say this, let it be a great passion and then death, rather
than a false or faked purpose.
So the lie in question is actually Lawrence not believing in P & N’s relationships being authentic - they must kid themselves!
2. Lawrence against Pierre.
What are the arguments against Pierre? At least for me Lawrence seems biased.
A book D. H. Lawrence's response to Russian literature by George John Zytaruk provides us with this piece of character analysis by Lawrence:
And War and Peace I call downright dishonourable, with that fat,
diluted Pierre for a hero, stuck up as preferable and desirable, when
everybody knows that he wasn't attractive, even to Tolstoi
Apparently, Lawrence was disappointed that he couldn’t establish the character’s relations to a toilet paper:
It will be recalled that for a character in a novel to be "quick”
means to "have a quick relatedness to all the other things in the
novel", and on this basis, says Lawrence, “Pierre, for example, in War
and Peace, is more dull and less quick than Prince André." Lawrence
elaborates:
Pierre is quite nicely related to ideas, tooth-paste, God,
people, foods, trains, silk-hats, sorrow, diphtheria, stars. But his
relation to snow and sunshine, cats, lightning and the phallus,
fuchsias and toilet paper, is sluggish and mussy. He's not quick
enough
It also looks like that he couldn’t believe that Natasha chose not the noble prince but the fat guy:
Of Natasha in War and Peace, Lawrence has little to say. This heroine
of Tolstoy's did not have the attraction for Lawrence that Anna
Karenina had. Since in Lawrence's mind Natasha is associated with
Pierre, whom she marries, Lawrence tars her with the same brush that
he uses on Tolstoy's hero. "One can't help feeling", says Lawrence,
“Natasha is rather mussy and unfresh, married to that Pierre"
Other epithets Pierre is awarded with are “domestic sort of house-dog” and “poor tool”.
3. Lawrence as a critic.
Essay The Literary Criticism of D. H. Lawrence by René Wellek opens with:
D. H. Lawrence is an extreme irrationalist
And his critical method is characterized as:
Characters are frequently discussed without any regard to their
function in a book, simply as human beings living today whom he
examines for their morals and asks for right behavior in a situation
abstracted from the book.
To conclude. My understanding is that Lawrence disliked the character and transferred these feelings onto his marriage.