Most phenylpropanoid standards are prepared in organic solvents mostly methanol due to their high solubility in the same. Once you have prepared your solution, minimize exposure to light so it would be store the lutein standard and any dilution thereof in brown amber bottles. Also -20C would be the best temperature to store it at. If you minimize the exposure to light and extreme temperature variations it should easily last a couple of months. Once the standard curve is out of your way, worrying about the storage might not be a big issue anyways.

Add a little quantity of antioxidant BHT (butylhidroxytoluene) to the standard solution

Lutein is a xanthophyll and  naturally occurring carotenoid. So basicaaly these are anti-oxidants. The best way is to store in amber bottle, under refrigerated conditions and should be avoided from light abuse like sunlight and heat. 

Lutein is well soluble in ethanol, rather stable in amber bottle, at -20C. The freezer should be lab type (not self-defrost, without light inside).