@roger,
Just put the
so in front of each that, to see which makes sense.
We have come to dedicate a portion of that field as a final resting place for those who here gave their live(s) (so) that that nation might live.
We have come to dedicate a portion of that field as a final resting place for those who here gave their live(s) that (so) that nation might live.
The first example works, the second doesn't.