stretching out forwards can very much help the lower back ime as well. When I first saw your photos, I knew right away that too much reach wasnt the issue, and actually thought that going forward could help. Without knowing where your seat is positioned on the rails, if it is in the middlish position, an easy way to experiment with stretching out your body a bit to see if it helps with lower back is to move the seat back a small amount, maybe a cm or so, and also at the same time rotate your bars slightly forward, which will bring the hoods slightly forward (your bars seem to have been rotated back a bit towards you).

My suggestion for this type of stuff is to ride with the needed allen keys and take a ride where you have time to make slight adjustments as you go along. Ie, keep it as is at the start of ride, then stop after 10-15 mins or whatever, make a slight adjustment of seat back and/or bar rotate, and you'll immediately feel if the change feels better or not. Until you get your adjustable stem on, at least this way you can see if slight changes help, costs nothing.

also, as Machka mentioned, small seat angle changes can help a bit too, although I personally find a level seat to be more comfortable than angled back like her and some others. Again, do changes one at a time and feel the difference. Doing while riding and taking breaks for changes to me is the best way, because you will immediately feel the changes and imo this helps better to properly evaluate if it is better or not. If a change is not good, you'll probably know in a min or two, so take your time and tweak as you go.

as you have gathered by now, getting your bike so it fits well is very personal, in the end you have to take the time and try stuff and be attentive. An allen key or two, taking the time, making small adjustments and just paying attention is the way to go.