In a food processor, whirl mango, 4 tbsp. honey, and the coconut milk until smooth. Taste and add more honey or the lemon juice if needed to balance flavor. Transfer to a glass measuring cup and stir in 1/2 cup shredded coconut. Pour into 8 (1/4 cup) fluted canelé* or popsicle molds, insert sticks, and freeze until solid, at least 6 hours.
To unmold if using canelé molds, dip molds in warm water, then pull popsicles straight out without twisting. If using popsicle molds, either let sit at room temperature 5 minutes or run molds under warm water 10 to 15 seconds. If you'd like a coconut coating, scatter 1/4 cup coconut on a piece of waxed paper. Roll and firmly press popsicles in coconut (outsides of popsicles must be slightly softened for it to stick). Serve immediately, or refreeze on waxed paper if serving later that day.
*We made these pops in canelé molds ($8 each; surlatable.com), typically used to make French pastries by the same name.
Make ahead: Up to 2 weeks, frozen.