It depends on your doctor's definition of "lie low." If your doctor is not suggesting surgery and you're wearing your brace as prescribed, you are probably safe to get up and do some light activity. Most doctors prefer not to have their patients simply lie in bed for long periods of time. Muscles weaken, joints stiffen, and many complications can develop, such as pneumonia, bed sores, and other problems.
There has been some controversy over whether it's safe to be mobile after having a fracture such as the one you've described. Some doctors suggest six weeks of bed rest; others want you up and moving wearing a brace. Recent research suggests that activity, including walking, is safe as early as the day of the injury, but only to the point of pain. At the very least, moving around prevents problems that sometimes come from long periods of bed rest.Â
Make certain you understand your doctor's definition of how much you can do. It's possible you're safe to get up and do tolerable activities now, but your doctor may want you to limit movement until he or she is certain your back is healing correctly.