This paper proposes a family of exactly solvable quasiperiodic lattice models with analytical complex mobility edges, which can incorporate mosaic modulations as a straightforward generalization. By sweeping a potential tuning parameter \(\delta\), the authors demonstrate an interesting butterfly-like spectra in the complex energy plane, depicting energy-dependent extended-localized transitions with a common exact non-Hermitian mobility edge (NHME). Using Avila’s global theory, they analytically calculate the Lyapunov exponents and determine the NHME exactly. For the minimal model without mosaic modulation, a compact analytic formula for the complex mobility edges is obtained, which, together with an analytical estimation of the range of the complex energy spectrum, gives the true mobility edge. The non-Hermitian mobility edge in the complex energy plane is further verified by numerical calculations of fractal dimension and spatial distribution of wave functions. Tuning the parameters of non-Hermitian potentials, the authors investigate the variations of the NHME and the corresponding butterfly spectra, exhibiting a richness of spectrum structures. The paper provides a detailed derivation of the NHME and discusses the effects of non-Hermiticity parameters on the spectrum structure.This paper proposes a family of exactly solvable quasiperiodic lattice models with analytical complex mobility edges, which can incorporate mosaic modulations as a straightforward generalization. By sweeping a potential tuning parameter \(\delta\), the authors demonstrate an interesting butterfly-like spectra in the complex energy plane, depicting energy-dependent extended-localized transitions with a common exact non-Hermitian mobility edge (NHME). Using Avila’s global theory, they analytically calculate the Lyapunov exponents and determine the NHME exactly. For the minimal model without mosaic modulation, a compact analytic formula for the complex mobility edges is obtained, which, together with an analytical estimation of the range of the complex energy spectrum, gives the true mobility edge. The non-Hermitian mobility edge in the complex energy plane is further verified by numerical calculations of fractal dimension and spatial distribution of wave functions. Tuning the parameters of non-Hermitian potentials, the authors investigate the variations of the NHME and the corresponding butterfly spectra, exhibiting a richness of spectrum structures. The paper provides a detailed derivation of the NHME and discusses the effects of non-Hermiticity parameters on the spectrum structure.