In a small saucepan, combine half of the blueberries with the sugar, water, and lemon juice. Simmer the mixture over medium heat for about 10 minutes, stirring occasionally.
Add the remaining half of the blueberries and cook for another 5 minutes, stirring now and then.
Remove the compote from the heat and allow it cool completely — the mixture will thicken and become jammy as it cools.