This study presents a family of exactly solvable quasiperiodic lattice models with complex mobility edges, which can incorporate mosaic modulations. By tuning a potential parameter δ, the authors demonstrate a butterfly-like spectrum in the complex energy plane, showing energy-dependent extended-localized transitions separated by a common non-Hermitian mobility edge (NHME). Using Avila's global theory, they analytically calculate the Lyapunov exponents and determine the NHMEs exactly. For the minimal model without mosaic modulation, they derive a compact analytical formula for the complex mobility edges, which, together with an estimation of the energy spectrum range, gives the true mobility edge. Numerical calculations of fractal dimension and wave function spatial distribution confirm the NHME in the complex energy plane. The authors also investigate variations of the NHME and butterfly spectra with non-Hermitian parameters, revealing rich spectrum structures. The models exhibit intriguing butterfly-like spectra in the complex energy plane, with extended and localized states separated by NHMEs. Tuning non-Hermitian parameters leads to changes in the NHMEs and deformation of the butterfly spectra, showcasing rich structures. The models can be extended to cases with mosaic modulations, and the analytical results provide a foundation for broadening the concept of mobility edges from real to complex planes. The study also includes numerical verification of the energy spectrum and NHMEs for different κ values, demonstrating the validity of the analytical results.This study presents a family of exactly solvable quasiperiodic lattice models with complex mobility edges, which can incorporate mosaic modulations. By tuning a potential parameter δ, the authors demonstrate a butterfly-like spectrum in the complex energy plane, showing energy-dependent extended-localized transitions separated by a common non-Hermitian mobility edge (NHME). Using Avila's global theory, they analytically calculate the Lyapunov exponents and determine the NHMEs exactly. For the minimal model without mosaic modulation, they derive a compact analytical formula for the complex mobility edges, which, together with an estimation of the energy spectrum range, gives the true mobility edge. Numerical calculations of fractal dimension and wave function spatial distribution confirm the NHME in the complex energy plane. The authors also investigate variations of the NHME and butterfly spectra with non-Hermitian parameters, revealing rich spectrum structures. The models exhibit intriguing butterfly-like spectra in the complex energy plane, with extended and localized states separated by NHMEs. Tuning non-Hermitian parameters leads to changes in the NHMEs and deformation of the butterfly spectra, showcasing rich structures. The models can be extended to cases with mosaic modulations, and the analytical results provide a foundation for broadening the concept of mobility edges from real to complex planes. The study also includes numerical verification of the energy spectrum and NHMEs for different κ values, demonstrating the validity of the analytical results.