Task-Free Continual Learning (TFCL) represents a challenging scenario for lifelong learning because the model, under this paradigm, does not access any task information. The Dynamic Expansion Model (DEM) has shown promising results in this scenario due to its scalability and generalisation power. However, DEM focuses only on addressing forgetting and ignores minimizing the model size, which limits its deployment in practical systems. In this work, we aim to simultaneously address network forgetting and model size optimization by developing the Lifelong Compression Mixture Model (LGMM) equipped with the Maximum Mean Discrepancy (MMD) based expansion criterion for model expansion. A diversity-aware sample selection approach is proposed to selectively store a variety of samples to promote information diversity among the components of the LGMM, which allows more knowledge to be captured with an appropriate model size. In order to avoid having multiple components with similar knowledge in the LGMM, we propose a data-free component discarding mechanism that evaluates a knowledge relation graph matrix describing the relevance between each pair of components. A greedy selection procedure is proposed to identify and remove the redundant components from the LGMM. The proposed discarding mechanism can be performed during or after the training. Experiments on different datasets show that LGMM achieves the best performance for TFCL.