Okay here goes....
Firstly I use this setup in mid-lane because Jax' ability to jump and stun can quite effectively out maneuver a ranged character. Secondly in lat game Jax' life-steal allows him to take on multiple champions maybe 2-3 at most unless the other team is really ****. Finally the change in Jax' E means that at low health the period where he dodges can be used to gain some health back.
The Runes I chose are primarily to help out early game where i feel that Jax can be easily outplayed to at least level 10.
(same as previous)
As the title says this build is about life-steal and Wriggles Lantern and Hextex Gunblade bring the life-steal up to 27% which is enough to last the rest of the game. These items aren't very effective until the attack speed items are bought and they then rake in ****loads of life-steal