The pelvis attaches to the lower back via the coccyx bone at the base of your spine, and to some extent it controls how hard our backs need to work to enable us to bend. Leaning forward on the bike not only needs our spine to flex, but also requires our pelvis to tilt forwards too. If you have a lot of stiffness through your pelvis, it won’t be able to tilt as far forwards as it needs to. This will cause the joints in your spine to overwork as they try to compensate for the stiffness in the pelvis. Over time, this can cause excess stress on the joints and eventually cause pain and/or injury.
If you have pre-existing low back pain which is unrelated to cycling, there is still hope of having a pain free ride! Your bike fit in this case would be vital to reduce the stress and load on your joints and muscles to reduce the risk of the pain occurring in the saddle.