We present the results of our analysis of a time series of high-resolution spectra of the multiple β Cephei star λ Scorpii. The data set has a total time-span of more than 5000 days and includes an intensive monitoring campaign during 8 consecutive nights. We confirm the presence of a dominant frequency f1 = 4.679410 c d-1 in the data. We show that the amplitude is variable in time according to the light-time effect in the multiple system. The dominant frequency is identified as a prograde dipole pulsation mode. From modelling of the amplitudes and phases across the profiles we derive pulsational parameters, the inclination angle 70° ≤ i ≤ 90° and v sin i ˜ 125 km s-1. From a comparison between theoretically calculated forcing eigenfrequencies induced by the close companion and the eigenfrequencies of the observed oscillation mode we find no tidal enhancement or excitation of the pulsation mode of λ Scorpii. We find indications for the presence of additional frequencies with low amplitudes. Based on observations obtained with the Coudé Echelle Spectrograph on the ESO CAT telescope and with the CORALIE Echelle Spectrograph on the 1.2-m Euler Swiss telescope, both situated at La Silla, Chile.