weeD

Yes, I'm having the same problem - either when I'm pulling someone over, finishing a callout etc. the game starts lagging, it's really weird. Perhaps one of the plugins gets stuck and overwhelms the game? 
I've disabled all of the plugins that I've been using, and my game did not lag at any point, so it must be one of the plugins that are causing the lags. 
Going to have to go through each plugin individually and see which one is causing the lags, I guess. :D

OK I took 6.0.0.3 out and installed 6.0.0.2 of traffic police and no lag! So it seems  if you want to use traffic police plugin 6.0.0.2 won't cause the lag. Also if you do downgrade that plugin and use any other plugin by Albo1125, remember you have to down grade those too because of the other files that comes with the plugin are updated with each release. both of these came out after the Ragehook.36 update so Traffic police 6.0.0.2 and arrest manager using RAGENativeUI 1.2 and Albo1125.Common 4.6.0.0 files. Hope this all makes sense.

I've been able to identify one problem - whenever I use the plugin Traffic Policer 6.0.0.3 and pull someone over once, it begins to lag whenever I try pulling someone else over. I will try perhaps downloading the plugin again or troubleshooting.
EDIT: been playing without the Traffic Policer plugin for quite a while - no lags at all.

Haha, pretty amazing. :D
However, I've tried turning on the plugins one by one - no matter what plugin I turned on, it seemed that the game starts lagging. I turn on one plugin, after like 15mins it starts lagging. Disable the one I turned on, activate a different one, same thing happens. The more plugins I have the faster the lag comes, but if I don't have any, the game never starts lagging. I don't even know what is going on. :D
If you come across any plugin that stops the lag please do tell me, maybe I have the wrong version of plugins or something, I am very confused. :D

Yep, That's my plan to, taking them all out running LSPDFR vanilla and look for lag and then add the plugins one by one until I find out what's happening.
Whats even more amazing is I have the same PC specs you have! lol