LIE-Te 8w7 sx/so here.
If you are ESI-Se 6w7 sx/sp, then you are the same type as a female artist whom I know. I really like her (OK, full disclosure, I think she's perfect), but she seems to be perfectly happy to be off on her own. She only contacts me when she wants to sell some of her art. She's interested in social justice and in leading people somewhere, but she's not sure where. I think the main impediment to her and I getting closer is that we both naturally want to lead and we are interested in completely different fields. I have been really frustrated with her in the past because she doesn't seem to see that we would make a great couple, but truthfully, if she doesn't see it, then I'm probably the one who is delusional in thinking otherwise.
I can easily see that she, like a typical e6, doesn't trust authority, including me, and yet she seeks someone to believe in. She calls me for advice but doesn't want to merge. An e8 is basically perfect for an e6, if the e6 can learn to trust the e8. However, she is not inclined to make that effort now, and maybe not ever.
I view her as being slightly too independent or scattered for me but I could easily see her with an LIE-Ni. Someone who just nods and says "Yes, dear."
I also know a male ESI-Se, probably also 6w7 but I don't know his instinct stack, whose interests overlap mine. He's smart as hell and has complementary skills in the sense that he's really great at taking a task and finishing it well and on time, neither of which I'm good at. He and I tend to talk over each other sometimes because we both want to be on stage, although perhaps for slightly different reasons. I like the guy. I think he'd make a great general manager but he works for someone else.
For about three years, I dated an LSI-Ti 6w5 female, probably so/sx, and we got along great in private and not so well in public. She kept trying to see who was in charge, but my approach to relationships is that neither of us is in charge. But once she decided that I was in charge (!!!), she stopped trying to dominate me and things settled down to a less stressful situation. She is older than either of the two ESI's mentioned above and has been married and divorced, so she might have better skills at making a relationship work and more motivation for doing so. Honestly, if she were ESI, I'd probably be married right now. But her Ti/Fe clashes low level constantly with my Te/Fi, and she has very hierarchical views on social systems, while I am basically outside most social systems.
To address your question about clashing with LIE's, yes, ESI-Se's do tend to occupy some of the same space as LIE-Te's, and therefore can butt heads to some degree. I'd say the relationship between ESI-Se and LIE-Te sub-types is better for public and work situations, while an ESI-Se might prefer an LIE-Ni for long term intimate relationships
. However, an LIE-Ni might seem a lot less appealing at work to an ESI-Se than an LIE-Te might.
There is a relationship calculator that you can use to get some sense of general compatibility between types and their subtypes. You can find it here: https://www.sociotype.com/tools/
I've been using it in real life for about five years, and I have to say, I find it remarkably accurate. It is even more accurate than you might expect a calculator which excludes enneagram and instincts might be, because the latter have less influence in relationships than Socionics type (IMO) and because those characterizations tend to track Sociotype in compatibility, to a great extent.