Lower back pain in prolapse patients can be due to the ligaments being stretched due to pelvic organs being out of place in the pelvic cavity.
Also, the pelvic floor muscles are attached to the tail bone so any downwards force due to prolapse/s can create tension and pain in that area as in other corresponding areas. Some Drs say prolapse is not painful but most prolapse patients do experience pain which can also be increased if you have hypertonic ( spasmy ) pelvic floor muscles.
See a womens physiotherapist to help you with pelvic floor strengthening and assessment of pelvic floor strength as well as other aspects in this area.
For diagnosis of prolapse see a Urogynecologist for an assessment and possible treatment options.