It sounds like you have a very nice pond. A UV sterilizer is a great idea to kill free floating algae. I believe you are saying you still have green water. If the UV light is not killing the algae then the water flow may be to fast for the light to work properly.
 
Yes, you do want to add a fine filter pad to remove the dead algae and other nutrients that are feeding the algae. This also means someone needs to clean the pads fairly often to remove the organic build up on the pads.
 
The carbon filter pad or a bag of activated carbon works great at removing organics from the water which can help get rid of the food source of algae too. Carbon also removes the tea color of the water which comes from leaves and sticks breaking down in your pond.
 
As you probably know live plants are great at competing for the same nutrients the algae needs. Many people use water hyacinths or other floating plants to shade the pond from the sun as well as they suck up a lot of nutrients from the water.
 
Lava rock traps a lot of organics in the pores of the rock. Bio balls are a much better choice since they are solid plastic. This will not have a great effect on free-floating algae but another step towards better water quality.
 
In your pond to get rid of the free-floating algae;
1. Make sure the water is not flowing to fast through your UV sterilizer.
2. Make sure there is good circulation in your pond. Good pond water flow will ensure all the water is eventually getting to the UV Sterilizer.
3. A fine pond filter pad. Pads clean regularly.
4. Live plants – floating and bunch plants.
 
I hope this gives you some guidance.
 
All the best,
Laurren
Aquatic Experts