Does sciatica always come from the lumbar region? Can you get sciatica radiating down the buttock to leg into the foot from nerve compression in the calf?

Sciatica. is not caused by nerve compression in the lower leg. You must have been issued a faulty owners manual. You had it right the first time. You can also get sciatica from compression of the nerve in the pelvis or upper thigh (in which case discomfort in the buttocks would not occur.
Lumbar issue. The sciatic nerve runs through the lower back, center of the buttocks and down toward the legs. This is an extremely large nerve, aggravated by lower back ( lumbar spine) issues.
From above. Pain shooting down the leg almost always is coming from above. See your doctor for an evaluation.