I think that most surgeons would not remove your implants while you are still lactating. There are potentially more complications at this time if you have surgery.
Your implants can be removed while lactating, but it would be best to be seen for proper planning. Depending on the placement of the implants and incisions this could be done under local anesthesia. Ideally it would be best to wait until you were done lactating. If your implants are saline, your surgeon could actually deflate your implants and remove all of the fluid and the implants could then be removed at a later date. There are risks with any procedure and these can be reviewed with with your surgeon. Good luck.
I think that it will be in your best interests to have the breast implants removed once you have completely stopped breast-feeding. Otherwise, you expose yourself to complications such as fluid/milk accumulation postoperatively. Furthermore, once you have stopped breast-feeding and reach a long-term stable weight, you will be better able to evaluate the long-term “status” of your breasts and make good decisions regarding the best breast operation to achieve your long-term goals. Best wishes.