Barley straw might help but takes a little while to establish the bacteria that hinders algae growth. First thing is to check your water parameters. High phosphates in the water will promote algae growth as will overstocking the pond and regardless of how good your filtration is, the algae will grow still. I am having a similar issue with my existing pond at the moment and putting it down to the sheer number of fish in it (was supposed to be temporary until end of summer last year but new pond still isn't finished, hence why they are still in there).
The lillys will come up eventually. A week ago, the lilly in the existing pond had no pads or runners coming off of it, now there are 5 pads on the surface (last year even with the blanket weed problem, the single lilly sprouted 26 pads!!!!!)