Do you know if any LapDock would do the trick?
Check This Linus Tech Tips use of TB2
If he could do this with TB2, with TB3 you can power even 100w (theory)
I plan to do this, but connecting it just to a Lapdock.
I still don't know if it would work. If it works with cell phones. Right?
Do you mean the HP Elite x3 LapDock? It's pretty expensive for what you get, unless you've found a supplier for less than $499.
I also own the Motorola LapDock. It's only 1366x768, but very portable and the battery lasts ~6 hours on a charge. With the right female-female adapters for micro USB and HDMI, you can use it with any normal PC. I won't say it's amazing, but I only paid 50€ for mine (new old stock) and for that price it's amazing.