Finding that running is causing a little pain in the lower back, i am going to say at the top of the illiac crest as it does feel about that sort of height. I haven’t been running very long and i accept that it is partially due to using muscles in ways they are not used to.

What are the possible causes and the possible solutions?

Literally hundreds of possible causes and solutions.

any chance of what are the most likely, and how they would be caused then, i can then think about what i am and am not doing to figure out what are the best ways forward.

Have you had a proper running shoe fitting session?

Poor core allowing your lumbar spine and sacroilliac joints to move around excessively, tight psoas major which would have a similar effect. Tight hamstrings, and tight erector spinae (the two big long muscles either side of your spine). Dodgy running gate. Weak glutes.

Basically due to a lack of conditioning.

Build up your running distance and more gradually.

As said above there can be numerous issues for me it’s the muscles surround my lower back. Bit of stretching to keep them in decent condition and that does help.

Tight hamstrings is my favourite from that list. Apparently they then tip your pelvis making the lower back sore. Stretch them out and also the muscles on your inner thigh.

SbZ i do suspect the problem is being a cyclist, and the resultant issues.