Lower back pain can be generated by the disc, facet, bone and nerve but in your case, I believe the differential is disc and facet. Standing/walking can lean more to facet than disc. Hopefully, the pain is more facetogenic than discogenic due to the easier treatment of facet pain.
The first step is physical therapy. a good course of 2-3 months can be helpful, especially if it is pilates based and you do your homework. If ineffective, then a series of diagnostic facet injections can reveal if the facets are the true culprit. If these blocks are effective (please read all hyperlinks to understand this and have the injectionist also read these), then you are a candidate for radio-frequency ablations (RFAs).