I'm currently doing my second degree at Mac in Stats, after doing a degree in Psych at another school. I know for Mac you can do a second degree if there isn't "substantial overlap" between the two programs... I'm quite sure you'll be fine getting into a Psych program because there isn't that much overlap between that and Life Sci, but I would double-check your potential new school's website or contact somebody just to be 100% sure. You just have to make sure you have the courses needed to get into the program (which I'm assuming for your case would just be intro psych).
Let me know if you have any more questions~