VRAM is used to load game textures and other data into the GPU where it can be processed the most quickly. VRAM usage goes up with increases in resolution and certain game settings.
Frame rates are linked to how many times the GPU can send out a complete frame of this data in one second. The less processing power that is needed to render a frame, the more frames can be rendered in one second. Thus, being able to reach 144 Hz is dependent on:
How fast your CPU and GPU is (cores, clock speed)
Compared to:
The amount of detail you are asking your GPU to render.
There is no direct correlation between VRAM and frame rates. If your games are causing you to run out of VRAM, that will reduce frame rates, but you do not need a specific...