Cell lineage tree is a model for the evolutionary history of cells sampled from an organism. Inference of cell lineage trees has been made possible by recent developments in single-cell sequencing. Accurate inference of cell lineage tree from large single cell data is a computational challenge. In this paper, we present ScisTree2, a fast and accurate cell lineage tree inference and genotype calling approach based on the infinite sites model. Compared to the original ScisTree, the main new feature of ScisTree2 is an accurate and efficient local search approach based on subtree prune and regraft (SPR) that is not implemented in the original ScisTree. To the best of our knowledge, ScisTree2 is the first model-based cell lineage tree inference and genotype calling approach that can work with very large data with, e.g., tens of thousands of cells.