Wash strawberries and cut off stems. Put berries in a pot with just enough water to cover and bring to a boil. Lower heat, put on a lid and simmer for 1 to 2 hours, until berries are formless and liquid is becoming syrupy. Put berries in a colander to strain juice into a glass bowl or other heatproof container. Let berries continue to drain into the bowl by covering the colander with plastic wrap and refrigerating overnight. (Alternatively, cook the strawberries on Day 2. After straining strawberries in a colander, gently press them with the back of a wooden spoon to extract more juice.) Discard berries.
After thoroughly washing lemons, slice each lengthwise into quarters. Then slice crossways as thin as you desire, removing seeds as you go. Place pieces in a glass bowl or nonreactive saucepan and cover with water 1 inch above fruit. Cover with plastic wrap and leave on counter overnight.
Boil lemon and water on high heat. Simmer for about 30 minutes, until the peel is tender.
If you cooked strawberries on Day 1, while lemon is cooking gently press berries in the colander with the back of a wooden spoon to extract juice. Set aside.
Remove lemons from heat and pour into a large mixing bowl. Add sugar, strained strawberry and lemon juices and stir well to dissolve sugar. (Taste and add more lemon juice, if desired. You want a balance of sweet and tart flavor.)
Transfer mixture back to large cooking pot. Boil over high heat, stirring often, about 35 minutes or more.
Test for doneness, and let cool for a few minutes before ladling into prepared jars.