Although turbulence plays a critical role in engines operated within low temperature combustion (LTC) regime, its interaction with chemistry on auto-ignition at low-ambient-temperature and lean-oxygen conditions remains inadequately understood. Therefore, it is worthwhile taking turbulence-chemistry interaction (TCI) into consideration in LTC engine simulation by employing advanced combustion models. In the present study, large eddy simulation (LES) coupled with linear eddy model (LEM) is performed to simulate the ignition process in n-heptane spray under engine-relevant conditions, known as Spray H. With LES, more details about unsteady spray flame could be captured compared to Reynolds-averaged Navier-Stokes equations (RANS). With LEM approach, both scalar fluctuation and turbulent mixing on sub-grid level are captured, accounting for the TCI. A skeletal mechanism is adopted in this numerical simulation, including 41 species and 124 reactions. Validations is carried out and numerical results show good agreement with experimental data. It is found that, Damköhler number (Da) at the onset of high temperature reaction evidently decreases as ambient temperature and oxygen reduces. Consequently, combustion mode varies from flamelet regime to slow chemistry regime, where the competitive effect between turbulent mixing and chemistry is more evident. Besides, scalar fluctuation has promoting effect on low temperature reaction, which is responsible for the over-prediction of ignition delay in low ambient temperature/oxygen condition without consideration of TCI. Further analysis of turbulence intensity on ignition is performed by using three different turbulence intensity. Contrary to what found in premixed combustion, ignition process in spray combustion will be promoted with enhanced small scale turbulence.