Allow me to save you an eternity of agony, a 2-word piece of advice: Give up.
Topaz have a truly excellent collection of add-ins, the problem is they never work in a consistent manner with 3rd party host applications. Use them in their in-house host application FX-lab, and all is in fine. You don't say whether or not you're also using Photoshop ( again a difference between CS6 and CC2015) - but if you are again there will be a difference in how/when the apps stall.
My experience is different to yours. Running Clarity, Detail, Infocus through Lightroom is fine (that 's with their obligatory FusionExpress2 intermediate host app). Use Edit-in ... and link to Photoshop produces inconsistent and unfathomable results - and no it's not an El Capitan issue - it's a Topaz issue, as can be seen by the sheer variety of incompatibilities that surface.
So you can appreciate the depth of the problem, I've attached two screenshots of what happens when I invoke the Topaz filter menu in Ps. The first run produces a clean list of apps, select one, Topaz loads and then freezes ( the ubiquitous spinning wheel). Force Quit is the only remedy. Try it again and your options are in the second screenshot ... Unfathomable.
Note to Topaz: You've got some excellent apps, they need work - life is too short.
Edit:
Make sure you have the latest version of their installers, all of which were upgraded to El Capitan. I know my results are different to your current experience, but for the record, the only way I can use the apps is by invoking them through Lightroom virtual copies and then loading the series as layers in Ps and masking accordingly.
Quite honestly, Manoli, I almost did give up.
I have been using Topaz through LR 6.3. After reading your post, I opened my Photoshop CS6. I did not see any special instructions to install in Photoshop. In the Filters menu, there was no Topaz Labs. I then physically copied the Topaz pluggins from the Library/Application Support/Topaz Labs sub folders. After closing and opening Photoshop the Topaz Lab apps appeared under Filters.
I did notice that while Lightroom is on 6.3, Updates in Photoshop CS6 show nothing new even though my Camera Raw is on 9.1, and as I open Photoshop from LR, I do get a message about the version mismatch. Are Camera Raw updates after 9.1 only for Photoshop CC?
What is so frustrating is the support. That ticket has been open for two weeks after several reminders. They just do not care. And this was the second such experience I have had with them. The first time I gave them a bad rating. Their reply was a bit optimistic, giving me a chance to change that rating:
"We're sorry to hear that you weren't satisfied with our response to your latest ticket: Unable to access Topaz Adjust5 or B&W 2.
At Topaz Labs, we truly strive to provide the best customer service experience that we can. Please take a moment to let us know if you have any suggestions that we can use in the future to avoid these poor experiences.
If you wish to change your rating or provide further details, you can do so with the links below:
How would you rate the support you received?
This ticket has been rated as Bad, I'm unsatisfied
You may still change your rating or comment."
Enjoy your day,
cortlander