What can I do for the fine lines underneath my eyes: Lower eye lid lift? (Photos)

Juvederm is a good product that is effective and has a place but not in the lower eyelid.  In my opinion it should also not be used along the lip edge.  Your eyes are beautiful.  If is essential that you not go out and do something that will damage your eyes and cripple you emotionally.  The lines are minor, and if you could like with them as they are that would be best.  However, if something needed to be done, I would start with a 35%TCA chemical peel.  Mind you I have not personally examined you so my opinion might change with an actual visit.  Does this mean that you should run out and get a lower eyelid chemical peel or a laser treatment?  You have to be careful.  Even individuals with very good credentials can get into trouble.  Many of the fractional laser treatments are mild so generally these are safe even if they do very little.Also I assume you are using an eye cream every day on this area which will provide mild help.  Good luck out there and stay safe.

Treatment for under eye fine lines is not surgery! Chemical peels or laser resurfacing is what u need. 

From the picture you present, you do not have significant eyelid lines.  what you are seeing is the crease just below the orbicularis muscle which helps you to blink and close your eye.  If these really bother you, you could try some laser resurfacing which should help to tighten the skin.  Surgery would help as well, but seems a bit extreme for the amount of excess skin you show here. See an oculoplastic surgeon for some advice.