Yes this was a big problem for me too. Some how the client got worse since recent patches but anyway as you guys say your computers are good it seems to me to be networking thats the problem which makes sense cuz its computer power independent. make sure you don't have stuff like bitTorrent running ( ending that process fixed for a lot of the lag for me )
open the task manager and go to the preformence tab, click the resource monitor button, and then go to the network tab in that. That should help show what is using most of your bandwith and u can start ending some stuff back in the procceses tab, careful tho if your new to this cuz it can do some harmfull stuff i believe
hope that helps, cuz playing a random champion because of network lag is sometimes pretty bad in free champ weekend lol