Took me a while to get it but Ryze

When i am safe from harm i pick up the pace until i come to harm

Miss Fourtune

Whenever some enemy dies close by, i heal for a percentage of their maximum health

Trundle.

My auto attack range increases each level

Tristoniën Justice (check sp4zie if you didn't yet)

I apply an annoying DoT every basic attack that stacks to 6

Darius.

If you let me hit you, I'll be closing in faster.

Sivir

40% of the time, my passive works all the time and I'll take less damage from your basic attacks.

Sion

If I kill you, I get some health and mana.

Cho'Gath?

My Passive gives me more power the farther down my health goes.

That's either Karma (increased AP based on missing health) or Olaf (increased attack speed based on missing health).

My passive, when triggered, allows me to ignore all CC and ability resource costs for a few seconds.