I'd look in to stretching and being more supple/ mobile. This should help you not tweak them as much.
But exercises to strengthen your back
Bent over rows
Deadlifts
Pull ups
Koing
Hey Koing, what kind of stretches do you do to increase back extension (i.e. arch)? Lay on a foam roller? Bridges?
You can't maintain a neutral spine with a curve in your lumber area?
What exercise or position do you want to get in to or improve? It would be tight hamstrings, hip flexors or a number of things which is causing you to not be able to arch your spine or keep it neutral.
Give some more info and I'll help you out
Koing
No, I want to be able to arch more. I can maintain a neutral spine just fine.
I see. I don't really get people to get a bigger arch.
I'd look at stretching your hip flexors. This will help give you a better arch. Leg swings, start slow and gentle then build up your pace as well as getting in to a lunge position, pushing your hips forwards and then leaning backwards for static holds will help.
Koing
Also, speedie, you can try this stretch, using a bed/couch/table:
I'll pick a PT table because this is how I was taught the stretch. For stretching your right hip, stand on the left side of the table, and place your right knee on it. Now, keeping your back straight, slowly kind of creep forward with your left leg, until you feel a good stretch in the right hip.
It's essentially the same as what Koing described above, which is kind of the classical hip flexor stretch. The one I just described allows you to go even deeper. Also, with the lunge position, I find it hard to do after leg day and I want to stretch out my hips as my quads are usually spent and I find it challenging to maintain good form & balance. Since I don't have a stretching table at home, I usually use the side of my bed.
Also, I will check with my g/f who is a PT, but I'm guessing you might want to form roll your lower back and stretch out your abs as well.