In a small pot, bring the water to a boil.
Stir in the sugar and simmer until the sugar has completely dissolved, then remove from heat.
Add the butterfly pea flowers, stir briefly, cover, and set aside for 30 minutes to infuse.
Strain the mixture through a fine mesh sieve into a medium bowl (preferably with a spout) and use the back of a spoon to press as much liquid as possible out of the flowers.
Carefully pour the mixture halfway up 6 popsicle molds.
Transfer the popsicle molds to the freezer to rest until starting to set, about 1 1/2 to 2 hours.
Stir the lemon juice and lemon zest into the remaining mixture in the bowl. The mixture should immediately change to a lighter purple. Cover and refrigerate the bowl until ready to assemble.
Once the popsicle molds are starting to set, top with the remaining lemon butterfly pea flower liquid in the bowl to the fill line.
Insert the popsicle sticks/cover and place the molds back in the freezer until completely chilled, 4 hours to overnight.
Serve immediately after removing from the freezer.