Cut the apple in quarters, core, then cut into bite-size pieces and sprinkle with the lemon juice.
In a small bowl mix together the sugar, cinnamon and nutmeg.
Add the cinnamon-sugar mixture to the apples and toss to coat all the pieces.
In a small sauté pan, melt the butter over medium heat.
When the butter is melted, add the apple mix to the pan and stir so all the apple pieces are coated with butter.
Cook, stirring occasionally until apples are tender and slightly caramelized.
While the apples are cooking put the oats, water, and salt in a small saucepan and bring to a boil.
Turn the heat to low and cook, uncovered, until oats are cooked through, 4-5 minutes.
If you like your oatmeal creamier, you may want to stir in the milk at this time.
When the oatmeal and apples are both done pour the oatmeal into serving bowls and top with the apple mixture.