Lag in games is one of the most annoying things that can happen.
The most common response from devs and gaming platform hosts, is that its connection lag.
The difference between server lag, connection lag and graphics lag is basic
Connection lag is caused by a players connection to the server and it involves factors like low bandwidth, heavy traffic on the connection route, weather, ISP issues, etc etc, its a long list....
Graphics lag is a issue with the graphics drivers, flash player, the PC software etc.....
SO in LoA II in the combat screen there is the speed and auto options
Speed will increase the speed of battles for those people that want to blink and the fights over. That does rely on a good PC and connection otherwise you may not see a difference.
More importantly, for players with lag issues or bad connections, is the Auto option, set that to on and the battle will auto play itself using the best options available with your heroes.... it does not mean it will use the skills when you think they should be used tho.
Mini client and browser. A mini client relies on up to date PCs, Internet explorer, flash player and graphics drivers/ cards. The most common reason for graphics lag can be the flash player and browser.
As the gaming world gets ready for browsers like Mozilla to drop flash and move on to html5 next year, we should see a improvement for players and their gaming experience.
Some browsers are prone to lag so its recommended that players try different browsers for their gaming experience, what may work for one, may not work for others.
Europe players do report a lot of lag issues and this has been confirmed as european connection issues, this is not the fault of the player, its simply their location and the connection to the servers, are over loaded with net traffic... the better option for them is a VPN which can reroute the traffic along a different connection and improve their gaming experience