Make margarita base: In a large glass measuring cup or pitcher, stir together lemon juice, sweetened condensed milk, water, tequila, and orange liqueur.
Divide 1/3 of the mixture among 5 paper cups
Pour 1/3 more of the margarita base into a blender and blend with frozen mango, adding more water by the tablespoon if necessary, until mixture is smooth and creamy. Divide among 5 more cups.
Rinse blender and pour remaining 1/3 of the margarita base into blender. Add strawberries and blend, adding more water by the tablespoon if necessary, until mixture is smooth and creamy. Divide mixture among the last 5 cups.
Insert a wooden spoon or popsicle stick into the center of each lime slice and top on each cup, making sure there is no room between the mixture and lime slice.
Freeze until solid, at least 5 hours.
When ready to serve, cut open cup with scissors and peel them away from the pops.