As already stated by KlausST, LSF0108 isn't a buffer. It just a number of pass switches limiting the bus voltage in one direction. Effectively a replacement for discrete MOSFET transistor used in this place.
A bidirectional buffer needs some kind of direction control, either external (the usual way) or with a special internal logic determining the signal direction from the signal levels and currents. There are some application specific buffers with automatic direction control available, e.g. for I2C busses. Besides respective higher price for the special logic, you pay a price in terms of performance.
For a parallel LCD bus, the R/W signal allows an easy control of DB data direction. All other signals are unidirectional and don't need direction control.