In the French LUNEX5 project (Laser à électrons libres Utilisant un Nouvel accélérateur pour l'exploitation du rayonnement X de 5ème génération), a compact advanced free-electron laser (FEL) is driven by either a superconducting linac or a laser-plasma accelerator that can deliver a 400-MeV electron beam. LUNEX5 aims to produce FEL radiation in the ultraviolet and extreme ultraviolet (EUV) range. To improve the longitudinal coherence of the FEL pulses and reduce the gain length, it will operate in Echo-Enabled Harmonic Generation (EEHG) seeding configuration. EEHG is a strongly nonlinear harmonic up-conversion process based on a two-seed laser interaction that enables to reach very high harmonics of the seed laser. Recent experimental demonstration of ECHO-75, starting from an infrared seed laser, was recently achieved at SLAC and is opened the way for EEHG scheme in the EUV and soft x-ray range. Furthermore, FELs are promising candidates for the next generation of lithography technology using EUV light. In this work, we report a preliminary study of EEHG scheme for LUNEX5 in order to reach the target wavelength of 13.5 nm, currently expected for application to lithography.