As a massage therapist, I have another answer for you. First of all, I saw where many people told you to place a pillow or support under your low back. That's not correct. The support needs to go under the bottom end of your tush. Although you may have a bit of a Lordosis, even if you don't, if you have enough of a tush, it will prevent you from laying with your back flat.
Since you feel a gap when you lay down on your back, you obviously have enough tush to interfere with your back laying flat. So you would have to lay with your knees bent, or put the pillow as I stated above.
However, there could be another thing affecting you. If you sit a lot, as in someone who is frequently on a computer, then you are already developing an issue that will cause low back pain. You are already contracting at the pelvic region, and that alone will cause low back pain.
Its like a seesaw. One side goes up and the other down. If you are somehow contracting in the pelvic region on a daily basis, that is the down. Contraction shortens the muscle and limits flexibility and range of motion. The opposite of this, then, would be overstretching; which is what would be happening to your back, because the front side is over-contracted.
It does sound like you have a Lordosis, but it could be exacerbated by over contraction on the front side, and overstretching on the backside. Stretching is a necessity, whether you work out or not, but if you workout, then your stretching needs to triple to accommodate the over contraction that you are doing in your workouts.
Now, usually, people having low back pain tend to bend forward to stretch the lower back. This is the wrong move. If the above conditions are the case, the stretch needs to be reversed because the psoas and the abdominal muscles are over-contracted and shortened. These need to be opened up. So the bend needs to be backwards.
One of the best stretches for this is to reach back and grab the ankle, making sure that you have something to help support you and the balance you need for this stretch. You grab the ankle and pull it up towards your tush as far as you can. At the same time, for an extended stretch, you bend forward, which is why you need something to hold for support. This stretch will open up the psoas, the abdominals, and also stretch your quads; which should take some of the pressure off your low back.