Room temperature measurements of the phonon dispersion relations in ferroelectric lithium niobate have been carried out by inelastic neutron scattering. Most of the measurements were made along the c* direction with two acoustic branches measured along an a* direction. The q to 0 slopes of the acoustic branches are found to be in good agreement with the ultrasonic sound velocity measurements. Results on the phonon frequencies are compared with the optical data. Measurements carried out at elevated temperatures up to 900K failed to detect any softening of the 'ferroelectric mode' (the lowest-frequency optic Gamma 1 mode), thereby suggesting that the ferroelectric phase transition in lithium niobate is not associated with a soft phonon-mode instability. The possibility that the phase transition is of the order-disorder type, rather than the displacive type, is discussed, and, in this respect, similarities with the isomorphous lithium tantalate are pointed out.