Just to be sure that I understand....
What is the reason or purpose for holding down the left mouse button while typing or pressing a key on the external keyboard?
Are you working with some application or game that uses holding down the left mouse button while pressing a keyboard key?
What game or app and what is supposed to happen or be happening with the left mouse button held down and a keyboard key pressed?
Are you using any Gaming or Ease of Access configurations via "WIN" +"I" and Gaming or Ease of Access?
More information is needed.
I'm afraid I cannot give you much information. I can tell you however that I discovered this problem first as a minor obstacle from Portal 2, and as a barrier in World of Warcraft. This is not limited to videogames as it can happen on the browser or even the desktop. It is clearly not an application limitation as much as a limitation set by the laptop somehow.
I have not performed any deliberate configurations to the computer that I know of. To rule out the issue of a mouse hardware malfunction, I used two different mice that worked just fine on another computer as a control. Again, I have no software that optimizes gaming through the modification of settings, nor have I modified the settings related to the mouse other then changing the palm rest for the touchpad, which did not change anything honestly, touchpad or external mouse.
To be the most specific, I can move the mouse around and even right click while doing this. However I cannot left click while pressing WASD (moving around in WoW) or any other key that I have tested.