Items like the Time in a Bottle (from Random Things) or the Imaginary Time Block (from QuantumStorage) work differently than the Lilypad. These items speed up the "Tile Entity" itself, which will effectively make the Botany Pot cycle faster.
[Lilypad of Fertility] ──(Sends Block Updates)──> [Standard Farmland] = Works [Lilypad of Fertility] ──(Sends Block Updates)──> [Botany Pot Entity] = Blocked 1. External Block Updates vs. Internal Timers does lilypad of fertility work with botany pots exclusive