You get lifeblade by progressing through the main storyline to the end of the krokosphinx. Talk to Sergeant Major Talbot after you've finished the last quest there.
Here's a straight answer: You need to finish Krokotopia before you receive your Life Blade.
On the other hand, the Life Trap is purchased on Colossus Boulvard in a Secret Shop next to Mindy PixieCrown. There are also a few more spells purchased there: the Reshuffle Spell for example.