How much of lower bike pain over longer rides due to bike fit or body positioning versus core strength? I have spent many years "fixing" my fit but have never had a professional fitting. I have also ebbed and flowed on my core strength over years and can't pin down it's role in "saving" my lower back pain over time.
This typically means that your drop is too significant or your reach is too far. Try moving your stem up once spacer and replacing the stem with one that is 10 mm shorter.
As other answers have noted, it would also be a good idea to get a professional bike fit since you've had chronic lower back pain for a number of years.
I often experienced lower back pain during and after rides on my roadie. Stretching helped me significantly. Try regularly stretching the muscles below, above and around your hip / bum, perhaps using hip-focussed yoga poses.
Your mileage is going to vary, and everyone is going to have different advice based on what worked for them. A professional fitting may be a very good idea. Also consider going to a doctor that specializes in this sort of thing.
As other answers have said, bike fit is important.
But a huge factor is also cadence. Even with a well-fitting bike, if you push gears that are too big for your core strength you will develop lower back discomfort and pain. Since you mention fluctuating core strength I suggest that concentrating on spinning at a higher cadence will help. Riding at a higher cadence always feels stange at first, but you'll get used to it.
If you start "bobbing", then concentrate on pedaling smoothly (ankling). Think of riding at a higher cadence like running a car at higher RPM. The higher the RPM the higher the power, but if you are riding at the same speed it also means lower force is going into each pedal stroke. And think how many steps per minute you would take if you were running. Not everybody would agree with me, but I say that 90 should be your slowest cadence (when you should change to a lower gear), with 100 as your average.
For practice, try this game. Ride with a friend, starting at, say 20 kph on the 34X17 gear. Now in the same gear find out how fast you can go. You will be surprised. Then try the next higher gear, and so on.
(parts of this answer come from this post of mine)
For me it often helps to change the position of the saddle up or down during the ride. Even if you lift or lower the saddle half a centimeter it can lead to a different position.
In the office I have lower back pain sometimes, changing the position of the body from time to time helps most times.
I think it is almost not possible to find the one and only bike setting for every time. Your body won't feel the same way every day of the year. Once you may have some stiffness in the neck without noticing it, but it can make you move different than other days at it can lead to for example lower back pain.
Oh, and I had lower back pain a few years always when I made sit-ups one time in last few days. I fixed that by stopping the sit-ups ;-)