Hey JKorzen,
I think what ever you do it would be a bad idea to raise your nutrients. I think what Sprung is implying is that this algae can grow in even low nutrient water. Do you test your nitrates and phosphates? From what i can tell Lyngbya is a filamentous cyanobacteria so it does need a bit of phosphate to survive. The best advice I can give you is manual removal and an attempt at introducing a few different types of grazers to see who will eat it. Sea Hare's might eat it but they don't have a good survival track record in captivity. Mine managed to get sucked through the strainer of my MaxiJet powerhead... quite unpleasant.
Good luck,
Kevin