For the raspberry sorbet, place the sugar and water into a saucepan and bring to the boil. Cook for 4-5 minutes, stirring occasionally, until the sugar has dissolved. Remove from the heat and set aside to cool.
Meanwhile, blend the raspberries and lemon juice in a food processor until smooth, then pass the mixture through a fine sieve. Mix in the cooled sugar syrup and blackberry liqueur.
Churn the mixture in an ice cream machine, according to the manufacturer’s instructions, until set. Transfer the sorbet into a freezer-proof container and chill in the freezer for 1-2 hours, or until set.
Preheat the oven to 160C/325F/Gas 3. For the crème brûlée, whisk together the egg yolks, caster sugar and vanilla seeds in a bowl until pale and fluffy.
Place the lactose free cream into a saucepan and heat until nearly at boiling point. Remove from the heat and whisk into the egg and sugar mixture until smooth. Pass the mixture through a fine sieve.
Place a layer of raspberries into the base of four 125ml/4½fl oz ramekins and pour in the crème brûlée mixture.
Place the ramekins into a deep-sided baking tray and place into the oven, then pour enough boiling water into the tin to come halfway-up the sides of the ramekins.
Bake for 30 minutes, or until the crème brûlées are set. Remove from the oven and set aside to cool before placing into the fridge to chill.
When chilled, sprinkle the tops of each crème brûlée with the demerara sugar. Place under a very hot grill or use a mini blowtorch to melt the sugar until caramelised and golden-brown. Set aside to cool completely before serving.