The exercises most often used to condition this area are deadlifts (regular and stiff-leg), good mornings, and hyperextensions. Of these, only the hyperextension movement has the potential to FULLY develop the lower back region. The reason for this can be attributed to one word: ISOLATION.
All other exercises will involve the glutes, hamstrings, or quadriceps and place the erector spinae (lower back muscles) in a stabilizing role. This means they are working isometrically and receiving resistance only in a nearly extended position.
The solution is to reverse this situation; place the hamstrings in a position to stabilize for the erector spinae - thus we have the hyperextension movement.
Identification of the proper exercise is only the first step; performing it correctly is the important one.
The first photo illustrates the proper form and technique. The trainee has the illiac crest (top of pelvic bones) lined up with the outside edge of the body cushion, putting the hamstrings in their stabilizing role and allowing the lower body to work from a full stretch to a complete contraction.
Photo two demonstrates how the movement should not be performed although many are doing it this way. You'll notice that the trainee has slid forward and is now contacting the upper thighs to the pad. Result: the pelvis is no longer stabilized, so the hamstrings get most of the work.
People are often baffled as to how the Russians can consistently excel in the strength demanding events. for one thing, they have been strong advocates of the hyperextension movement for many years now, and work up to holding close to 200 pounds behind the neck for reps!
Diligent, proper practice of this exercise will bring about nothing less than fantastic results, so go ahead and give it a try.
It will be the lower back exercise you are looking for.