Lung tumor's motion range has to be encompassed in segmenting the tumor volume and sub-volume to determine the internal target volume (ITV) and sub-ITV. The segmentation integrity of the ITVs influences the accuracy of treatment planning and dose computation. The goal of this study is to analyze lung tumor heterogeneity and respiratory motion effects on the segmentation accuracy of ITVs and sub-ITVs in four-dimensional positron emission computed tomography (4D-PET/CT) imaging using a novel 3D-printed variable-density lung phantom insert that replicates a typical heterogeneous tumor. The insert has an outer-volume and a sub-volume identified as a result of variable PET tracer uptake. The assembly of 3D-printed insert in the lung phantom filled with an __F-FDG solution was mounted on a programmable moving platform. Breathing waveforms were fed to the platform during the 4D-PET/CT acquisition. Two gating scenarios were investigated for contouring: during the end of expiration (gate (30-70)) or during the entire breathing period (gate (100)). Expected ITVs were calculated based on the known target dimensions and motion amplitudes then compared to their corresponding clinically segmented ITVs. We found that the clinical outer-ITVs contoured on 4D-CT matched the expected outer-ITVs for both gate (100) and gate (30-70) for all breathing waveforms, with a 2.28% discrepancy on average. While clinical sub-ITVs exceeded expected sub-ITVs by 36% in gate (100) and by 34% in gate (30-70). However, single-phase images of 4D-PET demonstrated to be nearly motion-free images, and segmentation of sub-ITVs in gate (30-70) reduced the discrepancy between clinical sub-ITVs and expected sub-ITVs by up to 60% relative to gate (100). Segmenting in gate (30-70) reduced intra-observer variability by 29% relative to gate (100). In conclusion, this work involved the design, construction, and end-to-end testing to validate a novel 3D-printed insert to study the segmentation of a heterogeneous lung tumor undergoing respiratory-induced motion in 4D-PET/CT imaging. Segmentation in gate (30- 70) achieved superior agreement between outer and sub-ITVs and corresponding expected ITVs. The PET limited spatial resolution and the fewer number of phases in 4D-PET binning (5 Phases) relative to 4D-CT binning (10 phases) are the major reasons for overestimating the clinical sub-ITVs.