Put 1/4 cup sugar, the salt, and 1 cup water into an 8- to 10-qt. pot. In several batches, peel, quarter, and core apples, then slice into wedges about 1/3 in. thick; drop into pot as you go.
Cook over medium-high heat, covered, until apples are very tender and begin to break down, 15 to 20 minutes, stirring occasionally. Remove from heat and mash with a potato masher. Taste and add more sugar or some lemon juice if you like.
MAKE AHEAD Up to 1 week, chilled airtight.