IME, cycling is the best back exercise there is. That said, position is important. Roll your pelvis forward and flatten your lower back. That might help. Try not pushing forward on the pedal as it goes over the top. That helps some people but not others. Do pull back on the pedal at the bottom of the stroke when climbing. That does engage the back muscles, but they have to get stronger anyway. Basically try riding more, especially climbs. A 90 minute climb is a long climb. That's gonna hurt. One can get stronger more efficiently by going hard on multiple shorter climbs, say 10--15', if those are available.

Other than that, yes, stretching is always good. So there are many different types of lower back weakness. Some are helped by squats, deadlifts, and stiff legged deadlifts Good tutorial on that last one is here:

One can address a different area of weakness with these tests and exercises:

I do all the above and it all helps, except that I do push forward going over the top, no problem there.