Been told I have a lipoma in my sternal notch. It's currently only about 1cm, but has tripled in size within about 6 weeks. Should I push for biopsy?

Maybe. My rule of thumb for soft tissue masses is if they are bothering you or enlarging, that's a good enough reason to remove them.
Tumor growth. The time frame for enlargement is not very likely with a benign fatty tumor, but more consistent with the accumulation of fluid in a cyst, or some other growth. Depending on the depth of origin, it could be just trivial, or possibly something serious. Perhaps you might consider getting an Ultrasound, or possibly a needle aspiration biopsy to guide the next steps.