Evenly scoop the ice cream into 4 dishes or decorative glasses and put in the freezer until ready to serve (this can be done up to 4 hours ahead).
Wash and pit the cherries. Put the cherries and sugar in a large skillet. Peel 2 strips of zest from the lemon in wide strips with a peeler and add to the cherries. Squeeze the juice of half the lemon over the top. Stir to combine evenly. Cover and cook the cherries over medium-low heat until the sugar dissolves, about 4 minutes. Uncover and cook over medium-high until cherries get juicy, about 5 minutes more.
To flambe the rum: If cooking over a gas flame, pull the pan off the heat and add the rum. Ignite the alcohol with a long match or one held with tongs. Swirl the pan slightly until the flames subside, about 30 seconds.
If cooking over an electric stove, put the rum in a small saucepan. Warm it over medium-low heat and carefully light it with a long match or one held with tongs. Pour the lit rum over the cherries, and swirl the pan lightly until the flames subside, about 30 seconds.
Ladle the cherries and their juices over prepared ice cream scoops. Serve immediately.
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