The G750JS Gaming Notebook has outputs of: HDMI, VGA/d-sub mini displayport, and mini Displayport.
The VG248QE has inputs of: HDMI, Dual-Link DVI, and Displayport.
HDMI runs at 60hz, so you won't be able to get 120/144 hz out of that. This leaves you with two options:
1. Mini Displayport to Displayport Cable (Displayport has enough bandwidth to drive the display at 144 hz)
This is your best bet for driving the display at 144 hz and getting the performance you want out of your monitor and GTX 870M.
2. Thunderbolt to Displayport/DVI-D
It may be possible to get 144 hz out of this configuration. The only downfall is that Thunderbolt is an Intel technology and is probably connected to your Core i7 integrated GPU. This means that you will not be getting the performance you want as it is not utilizing the GTX 870M.
TL;DR
Buy a male to male Mini Displayport to Displayport and use it.