In this work, an extension of the Flamelet Generated Manifold (FGM) method is developed suitable for igniting turbulent flames. To create the FGM, the strongly stretched flamelet equations (SSFE) are solved. Whereas in the standard basic method a single representative flamelet strain rate is used, in the new method a range of strain rates is taken into account. This allows including the effect of a varying turbulent scalar dissipation rate (SDR) during ignition. The new approach is validated by applying it in an Large Eddy Simulation (LES) of the Engine Combustion Network (ECN) Spray A turbulent flame for which detailed experimental data are available. First, in a priori validation step, the performance of the new extended FGM, the multi-strainrate FGM (mFGM), is validated by the simulation of ignition and species profiles in laminar flames along the so-called S-curve diagram and comparing with full chemistry calculations. The sub-grid scale (SGS) spray dispersion model is validated against the inert spray experiments in terms of vapor and liquid penetration as well as the spatial distribution of mixture fraction and its root mean square. Finally, the performance of the extended FGM is evaluated by comparison with the ECN Spray A flame. It is found that compared to the single-strain-rate FGM, the prediction of the ignition delay is improved considerably. This is related to the effect of the inclusion of the effect of the SDR, which is mainly on the second-stage ignition, i.e. the high-temperature chemistry. The low-temperature combustion is also affected as it occurs in richer mixtures than observed for the single-strain-rate FGM. Especially the formaldehyde, associated with low-temperature combustion, occurs in wider distribution. Finally, also predictions of soot evolution are studied. To improve the soot prediction capabilities, a new correction to the retrieved source term of the important pre-cursor, acetylene, is introduced. The above modeling developments have been made using a customized OpenFOAM solver developed by the authors. This work demonstrates the importance of including the SSFE SDR as independent parameter in an FGM based on igniting flamelets.