Open up your AirPort Utility.
1) 'Edit' your AirPort Extreme.
2) Go 'Wireless' tab.
3) Select 'Wireless Option...' at the bottom.
4) Check the box on the left of  '5GHz network name'.
5) Key in a network SSID for your 5GHz bandwidth.
6) Leave the 2.4Ghz and 5Ghz channel as 'Automatic'.
7) Hit Save, and the window will close.
8) Hit 'Update'.
You may quit AirPort Utiity.

Now, connect your ATV to this 5GHz network.
Try AirPlay again and see if it solve your lag AirPlay issue

The only way is to make sure your network is not congested.
Congested i mean here is there's no heavy internet user or multiple users sharing the same network at the same time.
It really depend how well the router manage to deal with the traffics. DIR-615 isn't doing well fyi.