Generalized Lyapunov equations play an important role in bilinear model order reduction and linear stochastic differential equations. They also arise solving generalized Riccati equations from stochastic control. In this paper we present a high-performance implementation of a Generalized Lyapunov equation solver based on the matrix sign function method for heterogeneous platforms, composed by a multi-core general purpose processor (multi-core CPU) and a hardware accelerator (graphics processing unit — GPU). Our CPU proposal shows runtime reductions of up to 5.2x over the original method, while a GPU-enabled version offers an extra speed-up near to 2.2x over the CPU counterpart, in a platform equipped with an NVIDIA GPU. Additionally, both variants show a good scalability on the problem dimension.