An extensive numerical study of two-phase flow inside the nozzle holes and the issuing jets for a multi-hole direct injection gasoline injector is presented. The injector geometry is representative of the Spray G nozzle, an eight-hole counter-bored injector, from the Engine Combustion Network (ECN). Homogeneous Relaxation Model (HRM) coupled with the mixture multiphase approach in the Eulerian framework has been utilized to capture the phase change phenomena inside the nozzle holes. Our previous studies have demonstrated that this approach is capable of capturing the effect of injection transients and thermodynamic conditions in the combustion chamber, by predicting phenomenon such as flash boiling. However, these simulations were expensive, especially if there is significant interest in predicting the spray behavior as well. This paper presents the development of a one-way Lagrangian approach for Gasoline Direct Injection (GDI) systems, wherein in-nozzle flow simulations can be performed with a small spray chamber domain and the results at the nozzle exit can be used to initialize a Lagrangian spray calculation. This coupled approach will account for the presence of phase-change induced voids at the nozzle exit and hence is expected to be more predictive compared to the standard blob injection model (which does not account for the in-nozzle phenomenon). Results are also compared against the standard Lagrangian simulations using the blob injection model which is initialized using rate of injection measurement (ROI). This work paves the way toward developing and validating a more predictive, but computationally tractable methodology to simulate GDI sprays.