Got me feeling old brehs
I had this problem for a long time. I never had any back issues playing ball, but every time I ran more than a mile my back would lock up. Finally last year I watched some running form videos on youtube (mainly from this channel Vo2maxProductions) and made a couple changes to my running form: straighten up my back when running (always look straight ahead, not down at your feet), eliminate hip drop which I did via a lot of glute exercises like bridges and hip pullthrus, and core work+stretching like others have said. Specifically hip flexor stretches have been helpful for me. Now i have no issues with my low back when running.
I have this issue due to some herniated discs. Do you have any other core and stretching exercises?
Funny thing is, I started a stretch routine yesterday.
Your running form could be an issue. If you slightly lean forward when you run, it can cause a sore lower back. Make sure you're running upright.