Missing/Dropped frames

I am having an issue with league. During the game I randomly get missing frames. An example is on vayne I go to get a last hit however the attack animation never completes and my projectile never appears on screen, but i still get the last hit. During this missing frame I am unable to input any controls. It could be a dropped packet as well. I am not sure whats causing this issue. Here are my computer and internet stats.

PC: i7 4770k 4.5 ghz 16 gb ram GTX 770 OC 250 gb SSD

Monitor: 144hz 1ms asus gaming monitor

Avg. 400 fps

Internet: Verizon fios 75 mb up, 75 mb down

Please let me know if there is something I can do to fix this. When I am trying to kite and loose control it is very frustrating.