Wont the lymphatic system eventually create antibodies that completely eliminate the virus in the body?
When polio causes paralysis it's because it has destroyed nervous system cells. Once those cells are destroyed they typically cannot be replaced, so it doesn't really matter what happens to the virus after that in terms of the immune system. See the Wikipedia page on polio:
In around 1 percent of infections, poliovirus spreads along certain nerve fiber pathways, preferentially replicating in and destroying motor neurons within the spinal cord, brain stem, or motor cortex. This leads to the development of paralytic poliomyelitis, the various forms of which (spinal, bulbar, and bulbospinal) vary only with the amount of neuronal damage and inflammation that occurs, and the region of the CNS affected.