Any form of chlorine can kill algae. I don't know what the 1 lb. packs from Lowe's are, but I suspect they are dichlor. All pools need some CYA but when it gets too high, then you need to keep your chlorine levels higher and higher in order to keep algae at bay. Some forms of chlorine are stabilized which means they have CYA (cyanuric acid) in them. Trichlor tabs (like what you put in a chlorine feeder) and dichlor powder are both stabilized.

Many people are not aware of the connection between CYA and needed chlorine levels. They use stabilized forms of chlorine for long periods of time and then don't keep their chlorine levels where they need them and then end up with algae. We see this all the time -- people who have algae and can't figure out why.

The reason I asked if you knew your CYA level is because if you knew that your CYA level was already high, I was going to recommend against using dichlor shock and instead using either bleach or pool store liquid chlorine (which is the same ingredient as bleach at a higher level and usually a MUCH higher price!)

You can read more about the CYA and chlorine connection in the Best Guess Chlorine Chart in my signature below.

EDIT to add that some pools (not all) lose all their CYA over the winter anyways so it may not matter.