I run TASServer on one computer, let's call it A. I connect to localhost with Spring Lobby on A. I host a new game on A. The other computer, B, connects to A's IP with Spring Lobby, sees the hosted game, and joins the game. When I start the game, however, B fails to connect to host.

If B hosts the game (on the lobby that A is serving) though, and A joins it, both connect just fine. (It also works if B runs the lobby server and A hosts the game.)

So obviously it's not a huge problem, because the work-around is easy, but still it is curious. There is one oddity about the network that might be causing this problem (I guess?). A and B are connected directly to each other via ethernet. (One is manually assigned 192.168.1.1, the other 192.168.1.2)

Any idea what's going on, anyone?

I don't know about the inner working of the tas server, but my guess is this:
TASServer will create the connection-info for B, telling it how to connect to A (-> script.txt). For that info it takes the IP of the connection coming from A. Now here is the thing: A connected to "localhost" - and that connection can only come from localhost :)
So my guess is, that B is told to connect to "localhost" - which doesn't succeed. To verify take a look at Bs "script.txt".
To circumvent the problem (if I'm right) A must connect to TAS through its own external interface (192.168.1.x). Then B will get sent that IP address for the game, and all should work fine.