I feel this has particular relevance in Brazilian Jiu Jitsu (BJJ) because lower back pain can be a common complaint from many BJJ and grappling practitioners. Whether caused by the sport or not, a big factor may be the constant flexion (or bent forward) position you see in the spine when in many positions. Strengthening the lower back once you've recovered from the initial injury could help prevent further problems in this area.
While common opinion may be that exercises like Romanian Deadlifts are effective in strengthening the lumbar extensors, this study references research that shows there is a greater stimulus to the hip extensors and not enough stimulus to the lumbar extensors. So deadlifts may not be the way to go when looking to target the lower back specifically.
The results of the study showed that of three test conditions, 1) control 2) kettlebell swings (KB) 3) isolated lumbar extension (ILE), only the KB and ILE group showed muscular fatigue, demonstrating both exercises placed physiological demand on the lumbar spine.
Of the two, the ILE (see image below on what ILE is) exercise did elicit the greatest levels of muscular fatigue, although I know I don't have one of those machines in my house and most gyms don't have these type of machines. Therefore, owning and using a kettlebell to elicit a similar response to work and therefore strengthen the lumbar spine seems like a very viable alternative for most people.
If you want to know how to do a kettlebell swing properly then looking no further than this site, I have an article here accompanied by a slow-mo video. Trust me, there are a lot of bad examples out there on how to swing a kettlebell. Take the time to read this article, it will pay dividends, it's a more detailed exercise than you'd think.
Edinborough, L., Fisher, J. P., & Steele, J. (2016). A Comparison of the Effect of Kettlebell Swings and Isolated Lumbar Extension Training on Acute Torque Production of the Lumbar Extensors. Journal of Strength and Conditioning Research, 30(5), 1189-1195. doi:10.1519/jsc.0000000000001215