Now seeing downtube42's post, it's totally normal for muscle exercise to produce soreness about 48 hour later, known and DOMS - Delayed Onset Muscle Soreness. It's normal, just means you did something unusual or did it more than has been usual recently. Since pedaling activity varies with the individual, the amount of activation of the posterior chain also varies. Those who activate that muscle chain on the bike are more likely to get a sore lower back from greater than usual cycling activity. That's a decent theory anyway, not a proven result.

That said, I've found that strengthening my whole posterior chain reduces or eliminates my back pain after riding. My favorite over time has been the Romanian deadlift, relatively light weight, high reps, a full stop at the bottom, no jerking. For this old man, say 40 reps with 100 lbs. but start with way, way less.