Combine blackberries, sugar, and water in a medium saucepan.
Mash and bring to a simmer.
Simmer 10 minutes, mashing periodically.
Strain syrup. Add in as much pulp as you would like (see note).
Add lemon juice and vanilla extract.
The amount of water you use will depend on how much of the blackberry pulp you add back in after straining it. Start with 1/2 cup and then after straining and adding the pulp, add more until it is your desired consistency, keeping in mind that it will thicken as it cools.