Can a transaction be conditioned on signing another transaction? I was thinking around http://lightning.network/ .

My problem is Alice sending coins to Bob via Eve: A -- tx1 -&gt; E -- tx2 -&gt; B

Is there a way to condition tx1 on Eve signing tx2?
Not directly, but you could do something similar by combining tx1 and tx2 into a single transaction.
So, instead of:

tx1:
Input         | Output
Alice (1 BTC) | Eve (1 BTC)

tx2:
Input          | Output
Eve (0.99 BTC) | Bob (0.99 BTC)


you could use:

tx:
Input          | Output
Alice (1 BTC)  | Eve (0.01 BTC)
               | Bob (0.99 BTC)


This doesn't seem useful for the lightning network, because you really don't want to have a payment fail just because a settlement somewhere along the path failed.