There is no medical reason why you cannot have lip filler during orthodontic treatment. One possible issue, however, is that the orthodontic treatment plan takes into account the position of the teeth in relation to the soft tissues of the face, including the lips, nose and chin. The shape, volume and projection of the lips can influence how the alignment of the teeth is planned. If your lips change during treatment, the orthodontic plan may need to be adjusted. For this reason, it is recommended that cosmetic soft-tissue treatments are done after orthodontic treatment is complete.
This answer is for general information. Your own case needs an examination by an orthodontist.