Fill a non-reactive bowl with water and acidulate it with the lemon halves. Rinse off quince and pat dry, then peel and place in lemon water. Once finished peeling all fruit, core each and return them to the lemon water.
Remove quince from the water, slice, and toss to combine with the sugar. Transfer the fruit and sugar to a heavy bottomed rondeau pot and cook over medium heat, stirring occasionally to prevent scorching. Cook for 2-2 ½ hours until the quince has softened and taken on a beautiful deep color. Stir in the lemon juice and cook for another 10 minutes.
Line a baking pan with plastic wrap and pack the quince paste into the form with a silicone spatula.
Allow the quince paste to cool completely, portion into blocks and wrap tightly in plastic wrap.
Membrillo may be stored refrigerated for up to three months safely.