Bring black currants and water to simmer; cook until fruit is soft. Strain fruit through a jelly bag overnight (do not squeeze bag, or juice will cloud).
Place strained juice, sugar, and lemon juice in a pot and heat until sugar dissolves. Simmer, stirring constantly, until droplets form sheet on a spoon (220 degrees on a candy thermometer). Pour into hot, sterilized jars, and seal.