Add the homemade coconut milk, strawberries, raw honey, fresh lemon juice, and optional homemade vanilla to the blender. Begin on low, then purée on high until the mixture is pale pink, completely smooth, evenly speckled, and pours in one steady ribbon. Stop once to scrape the sides if needed.
Set the clean mold on a level tray. Divide the mixture evenly among eight cavities, leaving about 1/4 inch headroom. Insert the sticks straight, wipe the rims, and tap the tray once to release a large air pocket.
Freeze on a level shelf for at least 3 hours, or until each pop feels rigid from tip to top and the stick does not wobble in soft mixture.
Warm only the outside of one mold cavity under warm water for 5 to 10 seconds. Pull the pop straight up, warming a few seconds longer if it resists. Serve immediately.