Heat oven to 180C/fan 160C/gas 4. Line a 20cm loose-bottomed or springform tin with baking parchment and stand it on a baking sheet.
Melt the lactose free butter and stir in the gluten free biscuit crumbs. Press the mix into the base of the tin, then bake for 10 mins. Remove from the oven and raise the temperature to 240C/fan 220C/gas 9.
For the filling, beat the soft lactose free cheese just until smooth with an electric hand mixer on low speed. Gradually add the sugar, also on a low speed, then the cornflour without overbeating.
Scrape the sides of the bowl. Slowly whisk in the lemon zest and juice, the vanilla, then the eggs. Scrape the sides of the bowl, then finally whisk in the lactose free cream. The mixture should be smooth and quite runny.
Pour the filling over the gluten free crumb base. Jiggle the tin to level the mix and squash surface bubbles with the back of a teaspoon.
Bake for 10 mins, then lower the heat to 110C/fan 90C/gas ¼. Bake another 25 mins and, if you are using an electric oven, leave the oven door slightly ajar for the first 3 mins.
After the 25 mins, shake the tin and there should be a wobble in the centre of the filling. If left until firmer it is more likely to crack later.
Turn off the oven, keep the door closed and leave the cake in for 2 hrs. Open the door, loosen the top edges of the cake with a round bladed knife, then leave in the oven to cool gently for another 1-1½ hrs.