We explore the dynamics of noninteracting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner. We find superdiffusion in position space for all parameters regimes. A directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time-driven potential. Magnitude and direction of the current are tunable. Several mechanisms for transient localization and trapping of particles in different wells of the driven unit cell are presented and analyzed.