Pour the peaches into the sauce pan and add the lemon juice. Bring to a boil, then reduce heat and simmer about 5 minutes. The peaches should turn mushy.
Blend the mixture with an immersion blender or in a jar blender until very smooth.
Return the pureed peaches to the pan and add the sugar, cinnamon, and nutmeg. Bring to a boil, then reduce the heat to low and simmer uncovered until the mixture is thick, about 25 minutes, stirring frequently.
Remove from heat and cool completely. Store in a jar in the refrigerator or freezer. Will keep for up to 3 weeks in the refrigerator and 3 to 4 months in the freezer.