The lemma says that in any configuration which starts finite and never dies out, there DOES exist at least one lifeline which DOESN'T go in a forbidden direction. (There are almost certainly lots of other lifelines which do go in forbidden directions, that's fine.)

An example of a lifeline in a southeastward spaceship that never goes S or SE: http://www.xamuel.com/images/lifeline.gif

The proof I outlined above was published in the Elect. J. of Combinatorics (last section): http://www.combinatorics.org/ojs/index.php/eljc/article/view...