I certainly can't speak for Lysis, and indeed probably can't really speak for most genderqueer or pansexual people, as I am neither.
That said, I have a very, very weak gender identity*, so I might be able to elucidate things a bit. Then again, as far as I can tell every person approaches their sexual identity rather differently, so this may well only be a description for me and me alone.
So. The concept I usually use when trying to describe transsexualism is imagining you woke up tomorrow as the opposite sex. Aliens, magic, whatever altered your body but didn't do a thing to your mind. Even getting past the initial shock of it all, it's fairly easy to say that your body would just be wrong, no?
Alright, so for, ah, agenderism that example doesn't really translate. So imagine, instead, that you'd lived your life up until now with no sex organs or differentiation: Your entire life you've been completely androgynous. Then you wake up to find that you're now male or female. It's not as...troubling as switching sexes, but it's still feeling wrong.
The problem with that example is that I'm not sure how accurate it is, since it implies a dislike of your sexual characteristics, which I don't think is universal for this situation. In my case, I'm a man, I have no real issue with that, but it also doesn't seem important to me at all, other than allowing me to grow my, rather silly-looking, soul-patch/goatee-thing. I hope that makes sense.
So, that's genderqueer. As it somewhat applies to me.
For pansexuality...I'm honestly not sure how it differs from bisexuality, so I'll leave that up to someone who knows more.
*Not so much active non-identification as...weak leaning, I guess? I identify as male, and I've no desire to cross-dress or similar, but if I woke up tomorrow in a woman's body it wouldn't bother me overmuch. Which, I know, goes against one of my examples up above, but I think that the idea of having one's sex changed against one's will is much more visceral to most people than it is to me.