In this work, we explore the application of a novel multi-domain spectral collocation method for solving general non-linear singular initial value differential equations of the Lane-Emden type. The proposed solution approach is a simple iterative approach that does not employ linearisation of the differential equations. Spectral collocation is used to discretise the iterative scheme to form matrix equations that are solved over a sequence of non-overlapping sub-intervals of the domain. Continuity conditions are used to advance the solution across the non-overlapping sub-intervals. Different LaneEmden equations that have been reported in the literature have been used for numerical experimentation. The results indicate that the method is very effective in solving LaneEmden type equations. Computational error analysis is presented to demonstrate the fast convergence and high accuracy of the method of solution.