Is it possible to fix my asymmetry with a reduction and lift?

Yes, based on your photographs, I think that a breast lift/reduction (if the lower breast is indeed larger), will help improve your breast symmetry. My best advice: select your plastic surgeon carefully. Make sure that he/she has significant experience achieving the types of outcomes you will be pleased with. Then, communicate your goals carefully, as discussed above. Working together you will come up with a good plan to achieve your goals. You may find the attached link ( dedicated to breast asymmetry concerns) helpful to you as you learn more.  Best wishes. 

As much as I am not a fan of "lifting" breasts with incisions around the areolas, I would suggest that you are a good candidate for correction of both breasts for best symmetry--the right breast would get a modest reduction and I would make the areola smaller, and on the left breast I would just make the areola smaller. This way your breasts would look the same. If you operate on 1 only they will look different for sure.