Is it normal to have two hard lumps at the very base of your spine?

Varies: There are a number of possibilities, some quite normal but i would encourage you to be checked if you have any concern. One example of a relatively normal condition like what you are describing involves the si joints. These joints are near the bottom of you spine on each side. They normally do have a small bursa over each of them and I have had patients come to be checked, but they are normal.