Turbulent lifted methane jet flames with various air-dilution levels and a range of inlet velocities are simulated. A partially premixed combustion model based on premixed flamelets with presumed joint Probability Density Function (PDF) is used. The joint PDF is obtained using a copula to include the statistical correlation between mixture fraction, Z, and progress variable, c. The non-premixed combustion effect is included using a simple algebraic model. Both steady and unsteady RANS simulations are performed. The steady simulations show that the computed lift-off heights agree well with measured values for a wide range of jet velocities and air-dilution level. Both of the Z-c correlation and non-premixed combustion effects are found to be important to get the correct lift-off height. Their individual and combined effects are analysed systematically. The unsteady RANS results indicate that multi-stage flame development, namely the initial expansion, flame brush development, its propagation and final stabilisation, is captured reasonably well in simulations. The various stages of temporal evolution of the flame brush edge is captured well and the agreement with experimental measurements is good.