Can I permanently lock certain chrome-tabs to the same desktop on Mac?
This is completely untested but just a couple of thoughts. 

Launching Apps on Login

For starters you can "pin" specific applications so that they will start on login to your account.

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Mission Control Spaces

You can then go into Mission Control and configure your screens so that they each have their own space.



Creating Spaces

Now access Mission Control (4 finger swipe up) and create a separate space for each screen. Now drag your applications to the corresponding space for a given screen.

NOTE: See here for reference: Use Mission Control on your Mac.

Pinning Chrome Tabs

Doing the above should get you most of the way to what you want. Pinning tabs in Chrome is possible as well. For example, you can right click on a given tab, and then pin it. Chrome will reopen these tabs each time you launch it and keep them in the order. 



Creating Multiple Chrome Windows

With Chrome, you can open up multiple windows with the pinned tabs in each, and then put each of these windows on a space for a given screen.

To open up multiple windows in Chrome:



References


Yosemite - Open App On Particular Screen