On average, how long will a lumbar spine sprain take to heal?

2-6 weeks: Minor sprains would need about 1-3 weeks, while more severe ones may take 4-6 weeks, as long as the correct diagnosis is a sprain only.

Sprain or strain: Sprain implies a tear to a ligament. Though unlikely without serious trauma, if stable should heal in 6-18 weeks. A strain is a soft tissue injury. From overuse to muscle tear, healing is in proportion to the damage. I would expect soreness to worsen 1-2 days then begin recovery over 1-3 weeks for most acute strains.