Gain-switched semiconductor laser technology provides a simple and low-cost method to generate optical frequency combs. However, the spectral coverage of these compact comb sources has been limited to the near-infrared range. Here, we combine a gain-switched laser comb with a continuous-wave translation laser within a periodically poled lithium niobate microresonator and demonstrate efficient and broadband sum-frequency conversion, spectrally translating the near-infrared comb to the visible domain. The broadband nature of the nonlinear conversion arises from a chirping of the domain inversion grating period along the microresonator circumference. We also validate the coherence of the visible-wavelength comb teeth which underlines the general applicability of this spectral translation approach.