Is there a connection between severe lower back pain and weak urine stream?

Yes: If you are taking pain medications that are narcotic, muscle relaxers, or other meds that have the potential to make you sleepy, then yes. If you had severe spinal cord/nerve compression, you likely would not be able to void voluntarily. There would be saddle numbness and likely pain into legs as well if related. So I am doubtful that you have cauda equina syndrome with only the 2 symptoms listed.