Dynamic lineage tracing technologies combine genome editing with single-cell sequencing to track cell divisions. We introduce Lineage Analysis via Maximum Likelihood (LAML) to infer a maximum likelihood time-resolved cell lineage tree under the Probabilistic Mixed-type Missing model, which we derive to describe key features of dynamic lineage tracing systems. LAML produces accurate tree topologies with branch lengths representing experimental time between ancestral cells. LAML outperforms existing methods in terms of accuracy and scalability on simulated data, and calculates the timing of cell migrations to metastatic sites in a mouse model of lung adenocarcinoma, revealing distinct epochs of metastasis progression.