If you're connected to their server, it's possible for them to execute commands on your client. Meaning they can change settings and key bindings as well as make you do many actions in-game.
It's unclear exactly what could be going on. But if they're executing commands on your client, there may be some settings they changed that simulates lag for you. The only ones that I can really think of that would cause this to happen are rate settings.
First off, you'll wanna verify integrity of game data to make sure that no files have gotten corrupted. To do so, go to your Steam Library and right click on Zombie Panic: Source. Go to the Local Files tab and click 'Verify Integrity of Game Cache'.
Next, In console check that all these cvars are at default setting or whatever you set them to: cl_cmdrate, cl_updaterate, rate
Lastly, the only other thing that I can really think of could be that they wrote some aliases on your client and it's spamming some commands or something every time you start the game up. If you don't know what an alias is in this situation don't worry about it. Just type 'alias' in console and if nothing pops up under it then you have no aliases written.
You didn't really mention that you tested out other games to see if they were lagging as well. It would be useful to give that a shot just to confirm it's only happening in ZPS. If none of those things seems to be the problem, you may have to reinstall (after backing up any files you may want like maps/models so you don't have to redownload custom content). Beyond that I'm not sure I can be much help.
If nothing works, then it is most likely a hardware/software problem or an issue with your connection. Be sure to do multiple speedtests throughout the day if you suspect your internet to be the issue. If you get big drops in the speed of your connection, you're getting throttled or need to replace lines or equipment. Contact your ISP if that's the case to have them troubleshoot it.
Otherwise make sure all drivers are up to date and that the physical inside of you PC case is cleaned out. Even a bit of dust and hair wrapped around the fans and heat syncs can cause heat to build up, more hair/dust to gather, and slow fans down. If you've owned your video card/processor for a long time, it might be time for some maintenance. The thermal paste between processor/video card and the heat sync can dry up and lose its ability to transfer heat. It's needs to be cleaned with rubbing alcohol and properly reapplied to keep your machine from over heating.
This is all I can really think of at the moment.