Good news everyone, I found a workaround - by having a custom application controling the fan speeds. I am capable of playing games properly, by just keeping the framerates locked to a certain point - constant 100% load obviously will have problems with keeping the GPU cold.
However, disclaimer - I am not responsible for any damage to your computer by using explained method,
You're doing everything at your own risk!!!
What I basically did was checking out software called "ThinkPad Fan Control" (link: TPFanControl - it is not authorised by Lenovo iirc) which is basically custom control to the fan speed of thinkpad laptops.
I found out that particularly version 062 fixes the issue if properly set.
Application, after installing and rebooting the system should start in the background with user login, if it doesn't just go to:
C:\Program Files\TPFanControl
and start the TPFanControl.exe file to make the application start. It should start in minimized mode to system icon, you should see new one displaying current mode. Double click it to run the main window:

There, you have three options.
- BIOS: System default. Here you have system defaults, select it to make application stop tampering with your laptop default fan settings. In my case State changes to 128, which seems to be indicator that indeed it is working normally again.
- Smart: Application's default. It enables the application to adjust fan speed accordingly to current temperatures. This setting has options for given temperatures in config file, as well as temperatures update frequency - everything is adjustable by user. Given temperature corresponds to given fan speed - going above certain level makes fan go with different speeds. I recommend having this one selected at all times since config file (if properly set) can get maximum performance as well as some degree of thermal security.
- Manual: Constant fan speed. System always has the same fan speed, regardless of temperatures. I'd recommend avoiding it since heavier load(especially on i7 models) will lead to higher emission of heat, and might lead to permanent damage (melting motherboard might quite a bit impact the computer's health...)
My Lenovo E590 has 7 fan speed levels, 0 being little to none of a fan running, 7 being an airplane sounding 4700 RPM. Current fan state is shown in State box of main window, having 128 additionally as BIOS default speed control signal.
Smart mode settings are all in one file:
C:\Program Files\TPFanControl\TPFanControl.ini
It has several settings that are meant for different laptops, I personally didn't bother yet to edit any of those.
The only change I made in my current settings is under Smart mode 1, having fan speed 7 on all temperatures, like here:
// profile "Smart Mode 1"
// change values and number of items for your needs
// Celsius: // Fahrenheit:
MenuLabelSM1=Smart Mode 1/ Label for Icon Menu, must be terminated by '/'
Level=60 7 // Level=140 0
Level=65 7 // Level=150 1
Level=75 7 // Level=165 3
Level=80 7 // Level=175 7
Level=90 7 // Level=195 64
This leads my laptop to ramp up fan to the max when starting to work. If I want it to be silent as usual, I just open up main window and select BIOS again to make it work silently and efficiently for all the other tasks.
Results are amazing, card works to its full potential, being throttled only when even the fan inside cant handle the load - and good example is keeping League of Legends on highest settings possible with no frame limiter. The normal work performance increased drastically too - processor is kept cooler as well, making it reach higher clocks without a hassle. This is all effect of this change - I didn't change thermal paste etc. myself yet - what should, in future, make it run even cooler than now.
Hope this helps you all too, at least until Lenovo decides to let users control their fans by default. Please let me know the results on different laptop versions - eX80, eX90, i5, i7 - all this data might help others too. I will check this thread from time to time and try to help, while enjoying Payday 2 with my new laptop ^^