Okay so I wanted to put my few cents in, if it may assist other stragglers like me. I spent a few times trying to fix this and I think I have now through reading through this forum to it's entireity but ended up having more issues such as USB power issues and such, and my mouse and keyboard were not working. And honestly this will take a fiddling reguardless and I believe may still fix the problem, but requires time and patience and persistence.

Step 1.) First you have to restart your computer. Entire Bios by pressing F1 and/or F2. Go to "Config" Than "Display" and switch it from "Hybrid" to "DISCREETE". Now exit and save changes.

Step 2.) Once your computer starts up you have to install 3 Lenovo Support Programs/Drivers. Go to the Lenovo Drivers page https://pcsupport.lenovo.com and download these three things.

1. Bios Update Utility (https://pcsupport.lenovo.com/by/en/products/LAPTOPS-AND-NETBOOKS/THINKPAD-P-SERIES-LAPTOPS/THINKPAD-P50/downloads/DS106108)
2. Thunderbolt software (https://pcsupport.lenovo.com/by/en/products/LAPTOPS-AND-NETBOOKS/THINKPAD-P-SERIES-LAPTOPS/THINKPAD-P50/downloads/DS105411)
3. Intel Alpine Ridge Thunderbolt Firmware (https://pcsupport.lenovo.com/by/en/products/LAPTOPS-AND-NETBOOKS/THINKPAD-P-SERIES-LAPTOPS/THINKPAD-P50/downloads/DS112986

Step.) Ok things are a little fuzzy from here in the order of installation, but I don't think it matters as much. It just takes a little fiddling around a bit. The first thing I did was install the Thunderbolt Firmware. The website the support staff provide was a little off. But this is how I did it. Once you open it up and click next, and after you uncheck install driver open up CMD administrator. Those unfamiliar with DOS/Linux commands this is where I had issues. As a briefing CD means (Change directory) CD.. (Goes back one directory) and Dir (Shows the folders and files, probably the most important command). In the solution on (https://support.lenovo.com/by/en/solutions/sf16-t0051) it says to type cd C:\DRIVERS\WIN\Thunderbolt_FW. When you type Dir in the C:\DRIVERS\WIN\ archive there was no Thunderbolt_FW, rather the default director was ThunderboltFW (with no underscore _). So for me you have to go to CD C:\DRIVERS\WIN\ThunderboltFW 

And so to install it you type in cmd FWUpdateTool.exe and follow the instructions. For some reason the solutions says to type Setup.bat, I do not see that anywhere, let alone the closest thing to that is actually for the Thunderbolt software NOT firmware which is Setup.msi

Now next you have to install the Thunderbolt Software. Install program but do not install the driver just like last time. We will do the same process. Go to command and type cd c:\Drivers\Win\Thunderbolt and then Dir. You will see a whole bunch of directories stuff.

Keep trying to repeat the same process. You also may switch your bios display settings back from Discreete to Hybrid. Note: Sometimes during bios flashing your laptop may continuously turn on and shut off. Try to attempt to remove the HDMI chord to do that. If you keep fiddling with these steps it should work. However it may also cause other issues as my power for my USB hubs went astray and a fix for that is to reset bios to default settings. I hope this helps people. I am not sure why the instructions weren't more specific. Cheers.

Kyle.

This has helped me! 
Force updating the ThunderBolt software resolved my problem. Thanks!

Unfortunately despite I managed to get the Thunderbolt software and firmware to work but I am still experiencing HDMI external monitor issues. It works for my other laptop which is the same model but not for mine. I am using Windows 10 it seems to still shut off when it goes to sleep and the NVIDIA control settings end up missing unless I disable and enable it. It is a fix, but not a very convienent. For the other laptop I am able to turn the external monitor on from sleep mode by just moving the mouse, I may have to turn my laptop in to replace the GPU either Intels or Nvidia, I am unsure. Any Lenovo administrators can you please help me fix this to resolve this issue? I am out of other options. Thank you.

After 29 pages of posts, one would think the issue on html connections would be fixed or least work arounds developed.

For me, the HTML connection seems to work ok for connecting to HDTVs, but not for PC desktop montitors.

Mine is a Dell 3840x2160 . 

Installing these updates works!

Thank you!

Want a simple solution for HDMI for Lenovo P50 not working?  This was the solution (SOLVED) that fixed my Lenovo P50 ThinkPad HDMI port.  Intermittantly, I would bring my laptop for presentations, and the HDMI port would not work with the projector.  When this would happen, I would use the MiniDisplay connector on the right side of the laptop, along with a HDMI or VGA adapter that I purchased, and would always bring with me to the presentation.  I tried the recommended steps in this forum, but for various reasons, they did not work.  Finally, on a whim, I typed in Device Manager into the Windows 10 search box, and then "Display adapters" - which I believe control the HDMI port.  I then did a "right click" on each of the adapter drivers (Intel Graphics and NVIDA Quadro), and selected "Update driver."  To my surprise, both needed updates.  Given that I ran Lenovo System Updates monthly, I assumed these drivers would be automatically updated as well.  Nonetheless, after updating these drivers, the HDMI port worked fine with multiple projectors.  I cannot say if this is a forever solution.  But I can say the other proposed solutions did not work for me, and this one did work for me.  Plus, it was really easy and took seconds to fix.  Hope this helps someone else!  If it does help, then please sign in and click on the orange "kudos" star below - thanks.

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 wrote:
I try with this, reinstall drivers for nvidia, intel 930 chipset. and nothing, still hdmi do not work. I am very disappointed with lenovo.
In may case, since feb/17 all work ok, and suddenly hdmi died, i waste last 2 days trying to fix. I can't work without the second screen.
I hope the solutions come soon, or p50 go the trash

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What is your second screen?  Brand/model?  Is there a reason you must connect using HDMI, rather than say DisplayPort?

Have you tried setting the BIOS to Config -> Display -> "discrete graphics"?  If you use your laptop plugged into wall power you might as well eliminate the built-in Intel HD Graphics for the laptop screen and just use the nVidia GPU 100%, for both laptop screen and external monitor.

Are you using a straight HDMI-HDMI cable?  Have you tried changing to a miniDP->HDMI cable?

My apoligies with Lenovo, in my case a vga-hdmi connector fail (i am using a very old monitor with only vga port). I realices when check the lenovo hdmi port directly with a hdmi device, and all is OK now.

Thank a lot.