Future wireless systems are envisioned to utilize the large spectra available at THz bands for wireless communications. Extremely massive multiple-input multiple-output (MIMO) antennas can be costly and power inefficient for wideband THz communications. An alternative antenna technology, which can achieve low cost and power efficient THz signaling, is based on leaky wave antennas (LWAs). In this paper, we explore the usage of the LWAs for wideband downlink multi-user THz communications. We propose a model for LWA-aided communication systems that faithfully captures the antenna operations. We that LWAs yield frequency-dependent beams, where the equivalent wideband channel induces dependence between angle, frequency, and spectral lobe width. We identify the LWAs inherent frequency-selective beamsteering capabilities as motivating multi-band THz communications that deviate from conventional orthogonal frequency-division, and employ non-identical subbands. Then, we propose an alternating optimization algorithm for jointly optimizing the LWA configuration along with the spectral division and power allocation to maximize the achievable sum-rate. Our numerical results show that a single LWA can generate diverse beampatterns, exhibiting performance comparable to costly fully digital MIMO. Interestingly, we demonstrate that allowing transmission with non-identical subbands leverages the characteristics of LWA-based channels compared to uniform division, yielding improved beamsteering that translate to higher rates.