Integration of sensors in textile garments requires the development of flexible conductive structures. In this work, cellulose-based woven lyocell fabrics were coated with copper during an electroless step, produced at 0.0284 M copper sulfate pentahydrate, 0.079 M potassium hydrogen L-tartrate, and 0.94 M formaldehyde concentrations. High concentrations led to high homogeneous copper reaction rates and the heterogeneous copper deposition process was diffusion controlled. Thus, the rate of copper deposition did not increase on the cellulose surface. Conductivity of copper coatings was investigated by the resistance with a four probe technique during fabric deformation. In cyclic tensile tests, the resistance of coated fabric (19 × 1.5 cm2) decreased from 13.2–3.7 Ω at 2.2% elongation. In flex tests, the resistance increased from 5.2–6.6 Ω after 5000 bending cycles. After repeated wetting and drying cycles, the resistance increased by 2.6 × 105. The resistance raised from 11–23 Ω/square with increasing relative humidity from 20–80%, which is likely due to hygroscopic expansion of fibers. This work improves the understanding of conductive copper coating on textiles and shows their applicability in flexible strain sensors.