Im getting these problems too. My ping remains stable at around 130 ms throughout the game, but at random times I would get these strange freezes where my character wouldnt respond to my actions. It would just stay there and if there where minions nearby, start aoutoattacking them.
Strangely enough, my ping remains the same during this freeze, and I can still see everything happening around me (life bars going down, receive gold if last hitted, screen turns red when receiving damage) even checking another lane out and seeing them kill a teammate of mine (with the corresponding "ally has been slain", with no lag at all)
This is very frustrating. Ive had to simply leave a game because I couldnt play at all. The delays would last up to 5 secs and would happen every 3-6 seconds at a time. Or sometimes I would get it once or twice during the game, or none at all. And all the time with 130 ms.