Lensless digital holographic microscopy (LDHM) offers very large field-of-view label-free imaging crucial, e.g., in high-throughput particle tracking and biomedical examination of cells and tissues. Compact layouts promote point-of-case and out-of-laboratory applications. The LDHM, based on the Gabor in-line holographic principle, is inherently spoiled by the twin-image effect, which complicates the quantitative analysis of reconstructed phase and amplitude maps. Popular family of solutions consists of numerical methods, which tend to minimize twin-image upon iterative process based on data redundancy. Additional hologram recordings are needed, and final results heavily depend on the algorithmic parameters, however. In this contribution we present a novel single-shot experimental-numerical twin-image removal technique for LDHM. It leverages two-source off-axis hologram recording deploying simple fiber splitter. Additionally, we introduce a novel phase retrieval numerical algorithm specifically tailored to the acquired holograms, that provides twin-image-free reconstruction without compromising the resolution. We quantitatively and qualitatively verify proposed method employing phase test target and cheek cells biosample. The results demonstrate that the proposed technique enables low-cost, out-of-laboratory LDHM imaging with enhanced precision, achieved through the elimination of twin-image errors. This advancement opens new avenues for more accurate technical and biomedical imaging applications using LDHM, particularly in scenarios where cost-effective and portable imaging solutions are desired.