I agree with manual removal - a lot of work, but low cost.
....not including the chiropractor's bill.
Seriously, when you physically remove the algae, simply drag it a short distance beyond the water's edge and let it dissicate for a day or two. At that point, the remnants will weigh 99% less than when you pulled it out - and should then be removed from the lake's watershed so the nutrients won't wash right back into the lake during the next rainfall event.
BTW: the lilies appear to be American Lotus (white bloom, large pad elevating above the water's surface with the supporting stem attached to the central area of the pad). Not positive of this id, since the image isn't overly detailed.
The shoreline plant looks to be one of the many species of primrose (yellow blooms, alternating leaves along the main stem).
