I had a low lying placenta until approx 38 weeks with DS2 - somewhere between 36 and 38 weeks it moved from being 2.5cm from the centre of my cervix (the "os") to minimum 4cm from my cervix. The sonographer was surprised but said it was entirely possible for it to happen. Generally as your bub grows "upward", it helps move the placenta up from the cervix.

My advice FWIW - don't worry about it until at least 32 weeks, and even then, if your placenta is still low lying, insist on having a further u/s (or two) closer to your EDD to be absolutely certain of its position.

A low lying placenta doesn't automatically mean a C-section. My great Ob was happy to let me have a natural birth even when the placenta was 2.5cm. However, her colleague would've greeted me at the birthing suite door with a scalpal. They're all different. I did several weeks of acupuncture (inc moxa) which probably helped me get the result I was hoping for.