Your lime is grafted quite high for a potted plant, but in the photos the graft is obscured by foliage. I mention this because the fast-growing shoot could possibly originate from below the graft point, and if so it is the rootstock and needs removing completely. Otherwise, it makes little difference where you cut it - or let it grow as suggested. Just depends on size and shape of tree you prefer. However, do make the cuts just a little above a leaf node, not leaving stubs several inches long which will never form new shoots or leaves.