The origin of twinning during the Czochralski (CZ) growth of 36°-RY lithium tantalate (LiTaO3) single crystals is examined, and it is shown that lineages composed of dislocation arrays act as an initiation site for twinning. Two types of lineages expand roughly along three different {12¯10} planes and two different {11¯00} planes. The former lineages and some latter lineages are composed of two types of mixed-dislocations with different Burgers vectors, while the other lineages are composed of only one type of edge-dislocation. All the dislocations have the Burgers vector of ⟨12¯10⟩ type with the compression side at the +Z side. Twin lamellae on {101¯2} are generated at a lineage during the CZ growth. We have hypothesized that dislocations in the lineage with b = 1/3⟨12¯10⟩ change their extension direction along a slip plane of {101¯2}, and they dissociate into pairs of partial dislocations with b = 1/6⟨22¯01⟩and 1/6⟨02¯21¯⟩ forming twin lamellae on {101¯2}.