For lemon butter, combine lemon juice and butter in a heavy-based saucepan and stir over low heat until butter melts. Whisk sugar, egg yolks and eggs in a bowl until combined, add to lemon juice mixture and stir continuously for 4-5 minutes or until mixture thickens slightly, transfer to a container and refrigerate until completely cold. Makes about 2 cups.
For lemon and thyme syrup, combine sugar, lemon juice and ¾ cup water in a small saucepan and stir over medium-high heat until sugar dissolves, add lemon zest and bring to the boil. Reduce heat to medium, simmer for 15-20 minutes or until zest is translucent, add thyme and simmer for another 2 minutes. Remove from heat, add limoncello and stir to combine. Cool completely.
Preheat oven to 160C. Using an electric mixer on high speed, whisk eggs, sugar and lemon rind for 7-8 minutes or until tripled in volume. Sift over flour, then fold through using a large metal spoon, add butter and thyme and fold through. Pour into a buttered and floured 28cm-diameter cake pan, filling to 3cm below rim (there may be mixture left over). Bake for 35-40 minutes or until golden and centre springs back when pressed gently with a fingertip. Cool for 5 minutes in pan, then transfer to a wire rack and cool completely.
To serve, halve cake horizontally, spread base with cream and lemon butter and sandwich with top. Scatter top with white sugar, drizzle syrup over and serve.