Broil chilies on a small baking sheet 3 to 4 inches from heat, turning as needed, until chilies are charred and blistered all over, 10 to 12 minutes. Cool. Remove and discard skin, stems, and seeds. Coarsely chop chilies.
In a 6- to 8-quart pan, combine mangoes, chilies, and lemon juice.
Mix pectin with 1/4 cup sugar and stir into mangoes. Bring to a rolling boil over high heat – keep stirring. Add remaining 3 3/4 cups sugar and stir until mixture returns to rolling boil. Stir and boil exactly 1 minute longer. Remove from heat.
Ladle into clean canning jars to within 1/8 inch of top. Wipe jar rims. Set clean, flat lids on top. Screw on bands. Invert jars for 5 minutes, and then turn upright. Let cool at least 24 hours. Check seals by pressing firmly on centers of the lids. If a lid pops back, it's not sealed; store it in refrigerator.**.
**Modern preserving guidelines call for leaving 1/4" headspace in the jars and boiling water bathing for five minutes at sea level. Remove to a protected countertop to cool, undisturbed, for 24 hours. Do not invert the jars as it can affect the sealing compound's ability to form a tight seal to the edge of the jar.