I have to agree with @Economist that EII-LSE duality is not really "natural". Together with LII-ESE, it is the least "natural" pairing; at least when it comes to people's dating standards in the real world, outside of Socionics.
I can take my own parents as examples here. My father is LSE, my mother is ESE. Neither one of them ended up with their Dual. Neither one of them "looks" or acts like their Dual.
My LSE father is additionally a Sp/So 3. My mother fit into the general beauty ideal in his culture. She was young, fit, blonde, blue-eyed, and merry. He was attracted to that, quite simply. (Most 3s are attracted to women who fit the cultural ideal, more or less.) When it comes to personality and thoughts, he does value the movies of EII film directors a lot, I have noticed. He introduced me to them years ago. He's also read a book written by an EII, and he almost never reads. So he does appreciate their work and thoughts a lot, but he wouldn't date anyone like them of course, being straight (they are all men).
Female EIIs in this day and age (and culture) are typically very "androgynous" in behavior and physical presentation, and very feminist. Most masculine or traditional men are not drawn to that. My LSE father is fairly traditional when it comes to what kind of appearance and behavior he likes in a woman. In my experience, most LSE men are rather traditional. A modern SJW EII would not fit into that. They wouldn't feel attracted. And their viewpoints would repel each other. For an EII, a traditional LSE with a "patriarchy-mindset" would turn into a Conflictor in their minds, simply because their Fi values are incompatible and opposing. It is no wonder most modern feminist EII women end up with a fellow Delta NF, or once in a while an SLI-Si in touch with their Fi, or an ESI-Fi. While most LSEs end up with an ISFx or SLI.