In low light, shutter speed will be slow. Unlike other cameras, L920 OIS lets you go down real slow like 1/3 or 1/10 seconds and still take good pictures. But moving objects will look blurred at such slow shutter speed. It's photography/physics 101. It's not camera's fault and you can't do anything about it.
Having said that, you can try to increase shutter speed by setting ISO to the max. Or use one of those app that let you manually control shutter speed. Picture will look more noisy though.
Yes, using flash is also an option.