Two main things apply here that affect the result you got.
When your camera meters a scene it assumes some of the scene is composed of lighter shades, some of it is composed of medium shades, and some of it is composed of darker shades. Absent of any instructions from you to the contrary, it will attempt to expose the scene so that the result is of medium brightness. But when you have a scene that is primarily white you probably don't want a medium gray result - you want the whites to look white. But your camera can't tell the difference between white and grey, and so it will normally expose for grey. You have to tell it to expose brighter using exposure compensation, probably at around +1.5 to +2 stops. The same is true of very dark objects, your camera can't tell grey from near black either. But in that case you need to dial in -1.5 to -2.0 stops of exposure compensation.
Fluorescent and some LED lights flicker. Not only does the brightness vary, but so does the temperature of the light. Peaks are bluer, valleys are yellower. Some people can actually see fluorescent lights flicker, but most of us can't. Cameras certainly can, though! If your images show the effects of flickering lights, the best way to combat this when neither the camera nor the subject is in motion is to reduce the ISO and aperture and use a longer shutter time. By catching several cycles of the peaks and valleys of the light flicker the light should even out. So if your image is showing the effects of flicker, slowing the shutter time down when possible will help.
In your image, though, I'm not convinced the variation in brightness is caused by light flicker. It may just be an indication that that your lights project an uneven pattern of brightness.
Even with the JPEG file, increasing brightness and using the eyedropper tool to "pick" the white balance gives a more natural looking result. If the raw file were available a true WB correction could be done. But WB is "baked in" when the data from the sensor is converted to JPEG. And the color cast near the hot spot in the upper right is another indication that you have uneven illumination from your lights.