I've done a 64km (924m elev) ride and just did a 19.8km (580m elev) ride. The first took 2:30hrs the later 1hr. I thought my lower back was sore because I have been on the same position for a while during the 2:30hrs ride but I realized I felt it a lot during ascension during the 20km one. The 20km ride was 5 climb of a small mountain near my home in town. I might be moving my back a bit too much when ascending.
I noticed I was pedaling slower on my highest gear than some folk who were passing me. I have no other option but to swing a bit every stroke which might cause too much movement on my back. This is just an assumption, I wonder if anybody have an other suggestion that could help me alleviate my problem?
I do "a lot" of ascension, about 800-900m every ride. I try to stand as much as I can to alleviate some other problems (bum soreness).

I did the bike fit myself. 145 knee angle and aligned with the pedal:
BikeFit - Road Bikes
It helped a lot but I guess there's something left to do!

I have had that problem. The fix was improving flexibility of the spine and raising the pitch or angle of my handlebars. If you are not flexible enough and your are way down on the bars you get lower back pain.

Try some yoga and adjusting the bars and see if that helps.

The shape of the Fizik Aliante R3 is meant to give more support to the lower back for less flexible people.

I've had this kind of problem, until I changed the way I pedal. I used to only stomp downward on the pedal, now I focus more on pushing forward (12-2 clock position) and backward (5-7 clock position)