Add the peaches to boiling water and cook for 2 minutes. Remove the peaches from the pot and immerse them immediately into cold water. When the peaches are cool enough to handle, remove the skins and stones. The skins will come off quite easily.
Mash the peaches into a pulp in a large mixing bowl. Add the strawberries and lemon juice and add it all to a food processor. Pureé the mixture in the food processor. Stir the sugar into the fruit mixture and pureé for another 10-15 seconds. Pour the mixture into a large, shallow dish and freeze until it becomes hard.