Subtypes ideally match, no matter what the specific ITR is.

Simply because preferred and emphasized IEs go better with each other.

LIE-Ni would hence be best with anyone whose subtype is either Se or Ni.

Aka ESI-Se and SEE-Se.
(And ILI-Ni, LIE-Ni, LSI-Se, EIE-Ni.*)

Now in real life, LIE and SEE is a rather uncommon pairing, no matter the subtypes. They are just too stubborn and keep fighting for the upper hand in the relationship. Generally, Gamma Extroverts do much better with introverted partners, afaik.

* Technically also IEI-Ni and SLE-Se, but the ITRs worsen the interaction. I wouldn't recommend those matches for romance.