Leg Press vs. Squat
Injured lifters gravitate towards the leg press machine as a substitute for the squat until things get better. But these two lifts are not biomechanically similar.
The leg press starts in a hip-flexed position and simply goes into a flexion so great that (ideally) the thigh is pressed right up against the torso with a knee flexion angle of around 90 degrees.
As an example, stand up and squat to mimic that exact position and you'll see how unfavorable it is for the low back. Though there's a minor save in the fact that the lifter has the load on his feet rather than his back, it's not enough to offset the fact that the lumbar spine likely goes into some deep flexion under heavier loads, especially if proper care isn't taken to watch form and technique.
Even with good form, we shouldn't forget that constant tension and shortening of the hip flexors, paired with the absence of hip extension due to the mechanics of the lift, creates residual low-back discomfort.
Do These Instead
Here are some better squat-free alternatives to the leg press that allow you to get a good lower body workout even if your back is getting cranky: