Welcome, Ambul!
If you want lilies, and other plants, for that matter, you will need a certain amount of sun each day.
I had full-sun issues, too, and that caused green water. What I did was to run heavy wires from the wooden fence to the house (my yard is very small, so this was only about 15' max length of wire), and then trained evergreen vines (bauer vine) to grow on it. The leaves shade the pond enough to reduce heat and algae, but I keep them pruned enough to allow sun to hit my lilies and bog plants.
And that same year, I invested in a pressurized bio filter, and that also helped take care of the algae, by correcting water conditions.
BTW, you can go to your profile and fix it so we can see under your user name where you live, and the gardening zone. That helps us know you better, and also to answer questions that may be related to climate.
Glad to have you!