This experimental investigation focuses on the gamma-ray interaction parameters and the buildup factor in lanthanide compounds (CeO2, Ce(SO4)2, Dy2(SO4)3, C3O9Sm2, C3Gd2O9, Pr2O3). These compounds were exposed to weak radioactive gamma sources with energies of 356, 511, 662, 1173, 1275, and 1332 keV by adopting narrow and broad beam geometry experimental arrangements. The incident and transmitted radiation intensities were measured using a NaI (Tl) detector. Experimentally measured values of mass attenuation coefficient and effective atomic number of lanthanide compounds were found to be in precise agreement with theoretical values obtained from NIST XCOM and Direct-Zeff database respectively. Additionally, the experimentally determined buildup factor values were compared with energy absorption buildup factor (EABF) and exposure buildup factor (EBF) values obtained from Phy-X/PSD software, providing insights into the gamma-ray penetration depth in terms of mean free path (MFP). At 356 keV, the EABF analysis showed that most compounds had a penetration depth of around 8 mean free paths. In contrast, the EBF analysis indicated penetration depths exceeding 10 mean free paths for all compounds except Ce (SO4)2. This new approach holds immense potential for transformative advancements in medical diagnostics, therapy, and the development of innovative technologies in nuclear sciences.