Mascerate blackberries in 2 T sugar for 5-10 minutes. If the berries are very tart, you may want to use slightly more sugar. Smash the berries using a fork until the mixture resembles a jam.
Stir half of the mixture into the softened cream cheese and add 1 T of sugar. Add additional blackberry mixture until a desired consistency is reached. Add in the lemon zest and any additional sugar if you would like the spread to be slightly sweeter.