The solution of large-scale Lyapunov equations is an important tool for the solution of several engineering problems arising in optimal control and model order reduction. In this work we investigate the case when the coefficient matrix of the equations presents a band structure. Exploiting the structure of this matrix we can achieve relevant reductions in the memory requirements and the number of floating-point operations. Additionally, the new solver efficiently leverages the parallelism of CPU-GPU platforms. Furthermore, it is integrated in the Lyapack library to facilitate its use. The new codes are evaluated on the solution of several benchmarks, exposing signifficant runtime reductions with respect to the original CPU version in Lyapack.