Well first of all i think a few numbers would help.. Make Nexuiz display the fps (frames per second) you can find it in the menu Options/Effects its called Show FPS. Thats mostly for your self so you monitor that value. For example some graphics drivers force vsync which can cause bad fps.
Then please open the ingame console by pressing shift-escape and enter tdem demo1 that will try to run that demo as fast as possible and report the line it outputs in the console after its finished.
Thats because when people report about lag its still had to say what exactly they mean.
Then please look at the scoreboard when playing by pressing tab and watch the values for Ping and PL (packetloss) if none are displayed they are too low (GOOD) otherwise PL should be small (best 0) and ping should also be low (not over 100).
Then it might be that some of your drivers cause some input lag. Try gl_finish 1 in the console and see if that helps. 0 is the default. If its not helping you might want to get it back.