Lattice dynamics of a single crystal of lawsonite were studied over a broad range of frequencies (1 Hz to 20 THz) using impedance, THz time-domain and infrared spectroscopies. Based on polarized spectra of complex permittivity hat{varepsilon } measured as a function of temperature between 10 K and 500 K, we analyzed the properties of the two known phase transitions—an antiferrodistortive one near T_{mathrm{c}1}=270,mathrm{K} and a ferroelectric one, occurring at T_{mathrm{c}2}=124,mathrm{K}. The former one is accompanied by a flat maximum in the THz-range permittivity hat{varepsilon }_{mathrm{c}} near T_{mathrm{c}1}, which is due to an overdamped polar excitation in the mathbf {E} parallel c spectra reflecting the dynamics of water and hydroxyl groups. The strength of this mode decreases on cooling below T_{mathrm{c}1}, and the mode vanishes below T_{mathrm{c}2} due to hydrogen ordering. At the pseudoproper ferroelectric phase transition, two independent anomalies in permittivity were observed. First, hat{varepsilon }_a exhibits a peak at T_{mathrm{c}2}=124,mathrm{K} due to critical slowing down of a relaxation in the GHz range. Second, infrared and THz spectra revealed an optical phonon softening towards T_{mathrm{c}2} which causes a smaller but pronounced maximum in hat{varepsilon }_b. Such anomaly, consisting in a soft mode polarized perpendicularly to the ferroelectric axis, is unusual in ferroelectrics.