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We numerically evaluate efficient wideband wavelength converters based on quasi-phase-matched cascaded sum and difference frequency generation (SFG + DFG) using step-chirped gratings (SCG) in lossy lithium niobate waveguides, and compare them to the ones using uniform gratings, assuming a large pump wavelength difference considering a full model of depleted pump and sum-frequency waves. For the same length, appropriate critical period shifts are presented for the number of sections and chirp steps to achieve flattop conversion efficiency responses with peak-to-peak ripples less than 0.2 dB. To obtain the maximum efficiency and flat response with a decreasing chirp step of 1 nm, the criteria for the design of optimum four-section single-pass and two-section double-pass SCG-based devices, including the assignment of length (to achieve a desired bandwidth) and pump power, are presented considering a 75-nm pump wavelength difference. Also, the performances of single-pass and double-pass schemes for the two- and four-section SCG-based devices are given, respectively, and compared to those of uniform grating-based devices with and without pump detuning, assuming a 3-cm-long waveguide and 50-mW input pump powers. For the same length and power, using the SCG with fixed pumps instead of the uniform grating with detuned pumps shows a noteworthy increase in the mean efficiency to attain almost the same response flatness and bandwidth.