My lower back is really stiff, most likely due to a stiff psoas (look it up to see if the pain originates in that area.) Based on your other sports activities without any pain, it's quite possible that your issue could be muscular. I was experiencing lower back pain last year, also in rides with a lot of climbing. I tried the following:

1. Let your back rest for several days until it feels normal again. In the meantime, move the saddle forward - You need to experiment with it a few millimeters at a time -- small adjustments.

2. Lowered the saddle about 1 cm. Again, you need to experiment after the first ride.

3. Warm-up for 20 mins. and stop for 2-3 mins. to stretch. This is important before attempting any long climbs. Stretch again on any break opportunity and upon finishing your ride.

Tried the above first. Another thing... Pay attention to your handlebar height if you suffer from stiff lower back. In my case, I can ride with the handlebar about 1" (max.) lower than my saddle. I tried 2" and it was too much (pain!!) With the new fitting, I still can keep up with my fast buddies who have more aggressive geometries.

If your pain is diminished after the first ride, you are on the right track, so make a few more adjustments. With my new geometry, I no longer experience back pain, except some discomfort if I'm off the bike for several weeks. It takes a week of riding (3x) with stretching to eliminate any discomfort again.

Hope it works for you, too!