A Breast Lift (Mastopexy) shapes and Lifts the breasts. It does NOT reduce them.
A Breast Reduction primarily reduces the breasts as well as Lifts them.
Your story is quite confusing. As I understand it ,you saw a Plastic surgeon with 34G breasts asking for a Breast Lift (NOT a Breast Reduction). That operation would have temporarily lifted the breasts (before they sagged again) BUT left them the SAME size (G). By your account, this is exactly what you were left with - G breasts.
Yet - you also state that the Plastic surgeon said he would reduce the breasts from G to approximately DD. That can be accomplished with a Breast Reduction NOT with a Breast Lift.
It sounds as if you had a Breast Lift NOT a Breast Reduction. Without examining your surgeon's operative report, it is impossible to tell what took place.
Now, it sounds like you are interested in a Breast Reduction after all. Obviously, there would have been less risks had the Breast Reduction been done in the first place. Each operation results in scarring and less blood supply to the breast skin and the nipple complex. As a result, the risks of wide scars, dead breast fat (fat necrosis) and even loss of the nipple complex may increase with each operation.
I would wait up to 6 months before having another breast operation. This would allow the circulation to the skin and nipple area to develop better and for surgical swelling to resolve. In the meantime you should discuss with your surgeon the long term goals.
In general, lifted or unlifted large breasts sag faster. A breast reduction would provide you with smaller, perkier breasts for a longer period of time.