A lattice-based scheme for the single-frame and the double-frame quantization of the speech line spectral frequency parameters is proposed. The lattice structure provides a low-complexity vector quantization framework, which is implemented using a trellis structure. In the single-frame scheme, the intraframe dependencies are exploited using a linear predictor. In the double-frame scheme, the parameters of two consecutive frames are jointly quantized and hence the interframe dependencies are also exploited. A switched scheme is also considered in which, lattice-based double-frame and single-frame quantization is performed for each two frame and the one which results in a lower distortion is chosen. Comparisons to the Split-VQ, the Multi-Stage VQ, the Trellis Coded Quantization, the interframe Block-Based Trellis Quantizer, and the interframe scheme used in IS-641 EFRC and the GSM AMR codec are provided. These results demonstrate the effectiveness of the proposed lattice-based quantization schemes, while maintaining a very low complexity. Finally, the issue of the robustness to channel errors is investigated