What position are you in when you are doing your exercises?
The reason I ask is this is the key to figuring out why the pain is occurring AND what you should do to make it feel better.
So someone on here says to do flutter kicks or leg lifts. Thats great if you can stabilize the spine while performing the exercise, but this stabilization is not easy because of the line of tension produced by an activated the psoas major.
The psoas major connects to the front of the spine and activates with hip flexion. This anatomical placement pulls on the spine with hip flexion. So if there is not stability within the spinal column, you will be repeatedly insulting the spine with each lift of the leg. Motion is produced at the point that is least stable. So what you may think is purely hip flexion may actually also have a great deal of extension in the low back.
Crunches are neither bad nor good, just realize what is happening. If you read the most current research by leading biomechanists, the message is repeated flexion of the spine can lead to early degradation of the disc. A crunch, therefore should be performed mostly with the thoracic spine (upper part of the spine not including the neck). You are working the rectus abdominus with this exercise with can be very provocative if you have discogenic low back pain, but it can also be relieving if you have irritation of nerve roots that are mechanically sensitize because this motion will open up the intervertebral foramen.
Planks can be good, but once again it depends. If you have a disc issue, the load produced by all the muscles can cause pain. Further the position itself can be provocative due to the level of extension present.
One more problem - there is no such thing as lower abs and upper abs. Maybe people mean the obliques? Or with reverse crunches they mistake the 'burn' of the psoas activation as the lower abs. if you look at an anatomy book you will see there is no separate lower ab (the abdominals surround the 'core' with muscle on the side) and the rectus abdominus (the only one on the front) does not activate separately (meaning rectus activation includes the upper and lower part). Just look at any study where EMG has been used with a situp or crunching task.
So the real question is what exercises are you doing and what motions cause your pain?
The best answer will be specific to what provokes your pain.