Is a breast reduction combined with a lift and implants a known procedure?

You ask a good question and one that I hear frequently from a different perceptive. While I can't speak to the intentions of those you received a consultation from, what each procedure means is a common question that can be clarified like this:
Reduction smallerAugmentation biggerLift elevated
You can lift and reduce size: that's a breast reduction, which virtually always includes a lift. You can lift and increase the size: that's an augmentation-mastopexy. You cannot, however, reduce the size and increase the size. That's like saying up is down and right is left. They're mutually exclusive. Where we most often encounter this question is patients sometimes ask if they can have a breast reduction covered by their insurance and then put in implants. That answer is always "no." You can get an augmentation-mastopexy, or "enlargement and lift," but this is not a reduction. A reduction removes tissue, lifts the nipple and areola, and leaves the breast smaller without the replacement of it with an implant.

Dear Fearless507109,
I understand your concern. It is best however that you consult with a board certified plastic surgeon to determine whether you can have several aesthetic surgeries in one session, as this would depend on various factors including but not limited to your general health condition, the type of anesthesia that will be used, and the type of surgeries that will be performed among others.
Daniel Barrett, MDCertified, American Board of Plastic SurgeryMember, American Society of Plastic SurgeryMember, American Society of Aesthetic Plastic Surgery

Thank you for your question.
This procedure is well known; however, without proper photos and evaluation it is difficult to say if this is the correct procedure for you. Oftentimes an augmentation in combination with these two procedures are to move the nipple into a more favorable position and to remove any excess skin. I recommend speaking with a board certified plastic surgeon to discuss your options.