Alright, here an update for everyone who is having a similar issue.
After getting obliterated by our squid, he actually asked for diagnostic files. After a lot of reboots (even using the sleep plugin, I am regulary using), I had no lags. And the reason is, I didn't reboot my PC as I normally do.
Normally, when I change VMs, or start stop them, I was using the android Array app. And as soon as I've run a test with booting from the array application, I got lags. I don't know what exactly is this app doing differently, but the result, at least for me, is lags.
Now I've purchased the android ControlR app and started the VMs a few times with it and didn't get any lags. So for me, the issue is solved.
