Would a lift and fat transfer solve issues? (Photo)

No, you need a lift to correct the sagging of your breasts. Implants do not correct sagging, but just increase volume.

Your best option is to add a breast lift and if you want to go up in size increase implant size.
There are some advantages to going submuscular but if there’s nothing wrong with your augmentation it’s probably better to keep the current implant position.
There are some inherent risks with doing an augmentation combined with a breast lift as a single procedure. Having had documentation done previously will reduce the chance of wound healing complications with the breast lift so there are some advantages to doing these as separate procedures.
Follow up with your provider to talk about surgery options or get a second opinion by having in person consultations with other board-certified plastic surgeons.
There’s no particular advantage to adding fat transfer if you already have implants.
Best,
Mats Hagstrom MD