Each modern LCD monitor has controls built into it that allow you to control which colors appear more vibrant on the screen than others. The colors you can pick from are usually only red, green, and blue with some higer-end monitors providing you with controls over slightly different colors. Each menu configuration is different for each vendor so I can't really direct you to the correct menu location but if you navigate through and adjust the color settings to balance out the colors and you're still getting a red tint thoughout the screen, there's a chance that you may have a damaged LCD panel which, on a consumer end, basically means that you'd have to replace the monitor entirely.

The only way to chalk this up to insurance would be if you could prove that it was indeed the lightning strike that caused the damage to the panel but you usually can't tell just by looking at the components. This being said, if you can prove that any other components, either connected to the computer or the surge protector (please know that a surge protector and power strip are two entirely different things!!!), were damaged at the time of the strike due to the lightning, then you have a pretty good shot at getting the insurance to cover it.