If you're starting from another color already, then first you should consult a color wheel, and then I'd suggest taking a a similar volume of water as is in your globe, and coloring it to match the starting color in your lamp, then I'd add the new color until the desired mix was achieved, and write down how much of the new color you had to add. IE, if your 32 oz. Now start adding your red until you get the desired shade of purple, and write down how much it took. This may sound like a lot of work, but you really don't want to wreck the fluid in your globe as its a fairly specifically engineered solution that would take considerably more effort to replace than it would to do a practice run and get it right the first time. Now add your food coloring to your now open globe.
Last step is the hardest, replacing the cap.
This is where I was worried of the possibility of breaking the glass, so I took much care here. I replaced the cap and pushed it down firmly, then I used the screwdriver and a pair of needlenose pliers to undo all the prying I did to get it off, pushing the edge of the cap back down around the lip of the bottle. Be careful not to squeeze the lip of the bottle with the pliers or slip with the screwdriver or you may break the glass. I don't know how easy it is to break, but theres no reason to find out. Last step is to take a pair of needlenose pliers and squeeze each of the little crimps in between the indentations.