Measure out fresh lemon juice, ensuring it's strained to remove seeds, and pour it into the blender.
Add granulated sugar to the lemon juice in the blender.
Pour in the ice cubes, either whole or crushed, into the blender.
Optional: add cold water to help achieve a smoother, more scoopable slushie consistency.
Blend the mixture on high speed until the ice is broken down into a fine, slushy texture, and the drink is frosty and well combined.
Check the texture; it should be thick, granular, and icy. If it's too loose, add a few more ice cubes and blend briefly.
Pour the lemonade slushie into glasses, garnishing with lemon slices if desired for a bright finish.
Serve immediately with a straw, enjoying the refreshing, icy tang.