In a large pot combine sugar, water and lemon juice.
One by one, peel and dice quinces. To prevent browning, add batches of diced quinces to the pot as soon as you dice them. Stir until integrated.
Bring to a boil on high, then bring the temperature down to low. Simmer for 60-75 minutes.* Instead of stirring carefully shake the pot every now and then.
As the foam starts to form on top of the quince syrup, remove as much as you can with a spoon.**
About 20 minutes before quince dessert is done heat oven to 390°F (200°C). Wash jars thoroughly with detergent, rinse and dry them. (If using walnuts, this is also the time to put them in the syrup.)
Place jars on a baking sheet and heat them for 15 minutes in the oven. (This will sterilize them.)
To check quince syrup for done-ness draw a line on the bottom of the pot with a spatula. Dessert is finished when the syrup is separating nicely (it'll be the consistency of honey, or lighter).
Carefully transfer the quince dessert into sterilized jars. Close jars and flip them until the jars and dessert cool down.
Serve with coffee, water or tea.