Direct lineage reprogramming involves the conversion of cellular identity. Single-cell technologies are useful for deconstructing the considerable heterogeneity that emerges during lineage conversion. However, lineage relationships are typically lost during cell processing, complicating trajectory reconstruction. Here we present 'CellTagging', a combinatorial cell-indexing methodology that enables parallel capture of clonal history and cell identity, in which sequential rounds of cell labelling enable the construction of multi-level lineage trees. CellTagging and longitudinal tracking of fibroblast to induced endoderm progenitor reprogramming reveals two distinct trajectories: one leading to successfully reprogrammed cells, and one leading to a 'dead-end' state, paths determined in the earliest stages of lineage conversion. We find that expression of a putative methyltransferase, Mettl7a1, is associated with the successful reprogramming trajectory; adding Mettl7a1 to the reprogramming cocktail increases the yield of induced endoderm progenitors. Together, these results demonstrate the utility of our lineage-tracing method for revealing the dynamics of direct reprogramming.