Blend strawberries, water, sugar, and lemon juice until smooth.
Strain to remove seeds if desired.
Fill popsicle molds one-third full with red mixture.
Freeze 1 hour until completely solid.
Mix vanilla yogurt, milk, sugar, and vanilla extract until smooth.
Pour white layer on top of frozen red layer. Fill to two-thirds full.
Freeze 1 hour until completely solid.
Blend blueberries, water, sugar, and lemon juice until smooth.
Strain if desired. Add blue food coloring if needed.
Pour blue layer on top of frozen white layer. Fill to top.
Insert popsicle sticks in center.
Freeze at least 2 hours or overnight until solid.
Run warm water over molds for 15 to 20 seconds to release.
Serve immediately or store in freezer up to 2 weeks.