Hi! I've been volunteering in a lab and have now been offered to my PhD there. I haven't done my final year project yet, so my question is: should I do it in my future PhD lab to get a head start on my PhD project, or should I choose another lab to get some new experience. (Field is biochemistry btw)

Probably best to do it in a different lab in order to broaden your experience. Ask your potential supervisor what they would recommend.