Esther Perel is fluent in English, and if you listen to her talk, you'll find her eloquent, but she makes a few non-idiomatic slips. In the paragraph above, she contrasts comfort with edge when she means edginess. Later on in the talk, in a passage you don't quote, she says "contract the gap", where "narrow the gap" would be more common.
In the passage you do quote, Ms Perel gives a list of contradictory qualities that she claims we have come to expect ("a given") in long-term relationships. Her thesis is that the contradictions drain the erotic energy from these relationships and that we think that
toys [i.e., sex toys] and lingerie are going to save us with that.
She's using with in the sense of concerning, which would be fine in a sentence like
toys and lingerie are going to involve us with that.
That must refer to the list of contradictions. It can't refer to toys and lingerie because that would take a reflective pronoun:
toys and lingerie are going to involve us by themselves
But the verb to save licenses the preposition from to indicate the dangers avoided, so we'd expect
toys and lingerie are going to save us from [all] that.
The preposition with combined with to save has the meaning of agency, so we say
the victim of the crash could have been saved with a seatbelt.
(Synonymous with the substitution of the preposition by) But the toys and lingerie are the agents of salvation, so using with leaves the uncomfortable sense that they are the antecedent to that in the phrase with that. Of course, the context makes it clear that this cannot be what Ms Perel means.