This paper advances a structural inter-temporal model of labour supply that is able to simulate the dynamics of labour supply in a continuous setting and to circumvent two main drawbacks of most of the existing models. The first limitation is the inability to incorporate individual heterogeneity as every agent is sharing the same parameters of the utility function. The second one is the strong assumption that individuals make decisions in a world of perfect certainty. Essentially, this paper offers an extension of marginal-utility-of-wealth-constant labour supply functions known as "Frisch functions" under certainty and uncertainty with homogenous and heterogeneous preferences. Two alternative models are proposed for capturing individual heterogeneity. First, a "fixed effect vector decomposition" model, which allows the individual specific effects to be correlated with the explanatory variables included in the labour supply model, and second, a mixed fixed and random coefficient model, which incorporates a higher degree of individual heterogeneity by specifying individual coefficients. Uncertainty is controlled for by introducing an expectation correction into the model. The validation of each simulation model is realized in comparison with the standard Heckman model. The lifetime models based on the fixed effect vector decomposition yield the most stable and unbiased simulation results, both under certainty and uncertainty. Due to its improved accuracy and stability, this lifetime labour supply model is particularly suitable for enhancing the performance of the pension models, thus providing a better reference for policymaking.