I've suffered from lower back problems for over ten years, and do get lower back pain on longer cycle rides.
There seems to be two schools of thought on how best to deal with this.
1. Ride In A Very Upright Position
Chiropractors and osteopaths would generally recommend that you ride in as upright position as possible, and argue that any curve of the back is a bad thing. This was certainly the view of my chiropractor and as a result I modified my bike so that I rode in a very upright position - however this never seems to resolve the problem.
2. Ride In A More Stretched Out Position
Following numerous favourable references on this forum to the bike fitting service provided by Paul Hewitt, I booked a session with him last year. He strongly advised me to change my riding position so that it was much more stretched out - his theory being that if you ride in a very upright position for any length of time all your upper body weight falls onto your lower back, whereas if are more stretched out more of your weight goes forward onto your hands.
I took Paul's advice and totally changed my riding position. However I have to say I have had mixed results - some rides are totally pain free, and others not so - and I think I need to experiment with my position a bit more.
Having said that I know that others have seen a big improvement after one of Paul's sessions, and other changes he made to my position definitely mean that my riding is now more efficient.
On balance I would recommend that you go see Paul, or someone who runs a similar service, and make sure your bike is set up properly. But you also need to make sure you look after your back, do regular back strengthening exercises, and recognise that you may get good days and bad days on your bike.