There are two easy methods to make this drink that are very similar. Which method you choose will depend on the kitchen gadgets you have on hand.
Method 1: combine 1 cup raspberries with 1 cup water in blender. Blend until as smooth as possible. Pour contents through a mesh strainer into a measuring cup, then through a funnel into a pitcher. If desired, strain the lemonade concentrate into the pitcher as well. Pour in 2 more cups of water, stir or shake. Serve over ice. Top off with raspberries if desired.
The second method is the same as seen in the lemon cheesecake recipe: How to make raspberry sauce. I just happened to have 1 cup of raspberry sauce leftover, that I had frozen. You can freeze raspberry sauce in an airtight container for up to a year.
Method 2: using thawed frozen raspberries, place 1 cup or more in a mesh strainer over a large bowl. Use a spoon to mash the raspberries against the strainer pushing out the juice into the bowl below. Continue this method until you have a pushed out all of the liquid from the raspberries. You will now have a raspberry puree in the bowl, discard remaining seeds and solid remnants. Mix 1 cup raspberry puree with 1 cup water. This will help dilute it and make it easier to pour. Using a funnel, carefully pour mixture into a pitcher. Strain lemonade concentrate, add to raspberry liquid. Add 2 more cups of water. Stir or shake. Serve over ice. Top off with raspberries if desired.