I had a low lying placenta as well at my 20 week scan. I have to have another one a 32 weeks to see if it's moved up.
My Ob said it is very common and there is about an 80% chance that it will move up and won't cause any issues. It all depends on where the placenta is attached to your uterus though. But at 20 weeks your uterus is still fairly small so there is a high chance of it being attched in a place that as your cervix grows your placenta moves away from your cervix.
If it is still low lying at the scan they give you in your 3rd trimester you'll most likely be told you'll have to have a c-section.