Well, to be blunt - and depending on the nature of your injury - if it is hurting when you change direction in the lift I would contend your bracing is not as good as you think it is.
I have problems with my lower back (caused by years of sports with no core strength) and the
only time I am not in pain is when I am lifting. Amusingly, the best therapy for when I have also strained those muscles (from lifting badly or picking up a piece of Lego) is to lift weight because it forces the muscles to behave in a structured way.