Okay, so I rely heavily on my client-side prediction, lag compensation and interpolation then. Maybe it´s even a good thing that lag even affects local games. That makes it waaay more easy to test and requires me to work really hard on the networking stuff, otherwise the game will suck for everyone, not just for the guys with slow internet speed.
Yes, you can also generate arbitrary latency for testing how it affects your game.
Usually your game update is staggered. First, Receiving packets, then updating your game (server or client), and finally sending your commands / states at the end of the update. It's one easy way to manage your game loop without adding unnecessary latency.
You can have a virtual network layer that can queue sending and / or receiving packets, as well as simulating packet loss, duplication and out of order (all of which should be invisible outside your lower network layer) for testing purposes, or if you lack the resources for proper internet testing. Then you can use renderless client-bots / servers, or just basic loopback networking with one player, like in Quake3 and many other Unreal / ID / Source games).