Use separate networks, upgrade your bandwidth/speed, consider consolidating back to one, take turns doing whatever it is online, or... Deal with it, to be quiet frank.

Hope to have helped!

You may not have strong or good enough internet connection to handle two consoles at the same time.

I would look into upgrading.

By the sounds of it, your connection must be quite slow and is unable to run both PlayStations online at the same time.

I often have 2 Ps4's on my connection and sometimes even 3 although my connection runs at a steady 50mbps at peak times.

The only logical thing I can suggest really is upgrading your connection to a higher package. Also, are both consoles using wireless? Your connection will become weaker if you are connecting them by wifi, try connecting them using an Ethernet cable, plugging one end into the back of your PS4 and the other end into a network port on your wall or to the back of your modem/router. This may reduce/remove the lag. You can also try disconnecting other wifi-connected systems which may be using some of your bandwidth such closing Skype, refrain from streaming music and videos and downloading anything while playing.

Could be your internet speed, could be your WiFi if both are on it. Could be multiple things, could always call your ISP for troubleshooting connections.

the more devices on one network equals more lag unless u have like really highspeed internet get another wifi or network setup and connect them two two diffrent networks

To connecting them with ethernet cable.. May help some.. but if your internet speeds aren't high enough it doesn't matter how you connect them.

like i said to another person lag is caused by your internet not being strong enough meaning your(not youre/are) isp giving you bad internet always use a ethernet cord make sure your internet is atleast 30mbs on psn

If you plug in an Ethernet cable to the ps4 does it use more data or it uses the same but better?