Just thought about this one when you mentioned lvl up. This is not luck, it's just a frickin amazing 14 year old kid calculating that a champion kill will give him enought for lvl 6. http://www.youtube.com/watch?v=pEmy70ezFTw
On topic. You are totally right with that the only things that can truly be called lucky are crits and phage procs. However. The title says "hate". I don't know, do you really HATE it when you win a duell with 1 hp and the enemy writes "omg lucky"? You will just seem very arogant and sound like a real douchebag if you say "No, not luck. I was more skilled than you." I agree with you that I get a bit mad at people using lucky to often. But the #1 will always be lucky and players are in my opinion alowed to write in all chat that I just got away with 1 hp.
A blind fired global ult into fog of war is very much skills and experiance I totally agree with that. Froggens lux ults are perfectly calculated even if the enemy might been out of sight for like 5 sec. I would hit 1 out of 50 of those, not because he is more lucky, but more skilled.
I am a Riven player myself. And I do a lot of cheese plays early using exp advantage. And I truly hate when some are like "Lucky kid, just hit 6". No, I plan to go in when I see that the last needed creep for lvl6 is about to die.
Very little is luck, but when it comes to the 1 hp thing. It is. Not theoretically, but nobody except you would call it skills to get away with 1 hp.