When considering range of motion issues with lumbar instability you need to ask,
What's causing instability to begin with?
Unless there was a direct trauma to a patient, like a brick falling directly onto their back, typically the answer is decreased range of motion.
Even if the patient had an injury where they bent forward to tie their shoe and herniated a disc, the likelihood is that the lumbar instability was there all along due to a lack of range of motion in the thoracic spine/rib cage and/or pelvis and hips.
The mechanism of tying a shoe was just the metaphorical straw that broke the camel's back.
When we have diminished range of motion we compensate in other areas that have a lot of range of motion.
When you think about the lumbar spine, it's surrounded by the rib cage and the thoracic spine above, both of which are very stable. Below we have the hip and the pelvis also two regions that are also known to be stable.
When you have decreased range of motion in these areas it only makes sense that the lumbar spine will compensate for the lack of range by moving excessively and becoming unstable.
The next component is that you need consider is that you need to have stability in order to have mobility.
When you have instability at a joint, particularly the lumbar spine it will affect all of the muscles that act in that particular area for two reasons.
When there's instability there's irritation and inflammation.
For every cubic centimeter of inflammation a muscle shuts down by 1%.
Therefore the muscles in that area will not be working optimally.
The second way that I look at instability with regard to muscular contraction is to think about a person trying to scale a building using a rope that is not tied to a fixed point on the roof of that building. This is what a muscle is doing when it is contracting against an unstable attachment point.
A person would not be able to climb that wall efficiently because the endpoint is not stable. Muscles work and contract in a similar fashion, if one of their endpoints is not stable they will also be inefficient in their ability to contract.
What I find with the majority of my patients is that it is likely that a lack of range of motion caused the instability to begin with and then the instability will negatively effect range of motion.
This is why people with instability become "stiff".
Therefore, in addition to treating the instability you also need to address the flexibility issues above and below that lumbar spine to prevent the instability from occurring again.
If you don't take away the cause you'll never take away the effect.