Can l5/s1 facet joint ligaments become lax?

Short answer: yes: Each segment of the spine is held together by the disc ;#40;shock absorber between the bones up front;#41; and the ligaments in the back ;#40;facet capsules, inter- and supraspinous;#41;. As the spine wears out ;#40;spinal degeneration;#41; both the discs and ligaments can become less stable, less supportive, and lax. This can lead to forward slippage of one bone over the next, called spondylolisthesis.

Yes: If you are not working on your core muscles, overtime your ligaments in the spine can get lax resulting in extra wear/tear on the spine causing arthritis or pain in the facet joints.