The things I took from Barter back when LT was a replacement project (i.e. when Barter was no longer accepting logins and had lost most of its users) were the things that made sense and were usable. Everything that's not like Barter is just me saying at one point, "okay, this can be improved."
So, yeah, the fact that LT doesn't have collapsible menus for offer creation is a deliberate choice. (Just like the fact that there's no 'Fail' button on offers for now. Although I'll have to handle that as well ASAP.) The main reason is that most browsers don't bother to auto-open them when you're searching for a game name in particular, so at worst the browser will act as if the game wasn't found, and at best it'll show you the game, but in a collapsed list and as such it highlights an invisible part of the page (e.g. long reviews on Steam.)
Currently I'm leaning towards a dropdown indicating what games can be listed. Dunno if it'll be remembered across users. Also dunno if I'll reload the lists through Ajax or directly the page. (Ajax is longer to implement. Although I can reuse most of the code I wrote for my Ajax implementation of the bottom half of the offer creation page.)
Or you could list all the games and then have tags/colors next to games you already own, games you have available for trade, etc.
Yes, I know, I'm already doing it in some situations, and if I end up showing all games I'll always do it, but it doesn't change the fact that page loading can get really, really long when one of the parties has a huge library. LT is hosted on a top-notch server, it's fast as hell, but it still has to send you the data. ;)