I figured out how to attack - press "F" I think it was to equip a gun.
I think the aiming mechanic is a bit back to front but the idea is good. When you are trying to shoot enemies, Lana aims based on movement rather than where your mouse may be or any other form of control. It made killing zombies rather challenging, but if this mechanic was improved, I think the gameplay experience would be better.
Edit - I killed 3 Zombies.