A kill lane is essentially a lane that poses no threat to you. Effectively, you own the lane and no one can stop you so you Snowball. in some cases you can go 7/1 in 8 minutes. An example of this is Teemo Blitzcrank Where even if Blitzcrank manages to Rocket Grab you, Teemo has such poor scaling early game, hes pretty easy to out duel.

A Death lane is the opposite. Where you can get Bullied or Zoned out of Gold/CS/Experience. If you do get brave and try to CS, Often times you will be hard Crowd Controlled and have a large chunk of your health gone. A famous example is Lucian Blitzcrank. Were blitz Rocket Grabs you in, Lucian Relentless Pursuits into you, gaining his Light Slinger passive Blitz Proceedes to Power Fist, throwing you up into the air. Lucian hits you with Piercing light, again gaining his passive Blitz Activates his Ult (Static field)Silencing you, Lucian hits you with Ardent blaze, gaining his passive and movespeed as that is what attacking a target with Ardent Blaze does. This combo Ether can flat out kill you at level 3 or force you to recall Losing gold, EXP, and Minions and in general force you to fall behind.