I'm a dyke, and I'm kinda unclear as to what a "lesbian relationship" is. If I had to define it as it stands, I would guess that it's a relationship comprised entirely of lesbians. Everyone involved is a lesbian.
I like the term "same sex" relationship- it tells you this is a relationship between two people of the same sex, without referencing the sexual orientation of either one. Because sexual orientations tend to fluctuate for lots of women, it gives people a way to reference or name the relationship that they are in or desire to be in without making them commit to a complete change of identity. You can easily enter into a same sex relationship with a woman without having to adopt the lesbian identity.
I also like the term "queer"- which to me indicates things that are non-normative. Queer is the overarching current that touches all of my interactions. The women I have relationships with are queer. I even find that I can enjoy certain kinds of interactions with men, but only if those men are also queer.
Regarding pansexual- I like this term, but I agree, it's hard for most people to understand or explain. Here is my best approximation: Pansexuality is basically like bisexuality with the acknowledgement that there are more than two genders.