Recent data indicate that lead (Pb) can induce adverse effects even at low exposure levels. Moreover, the corresponding mechanisms of low Pb toxicity have not been well identified. In the liver and the kidneys, Pb was found to induce various toxic mechanisms leading to organ physiological disruption. Therefore, the purpose of the study was to simulate low-dose Pb exposure in an animal model with the aim of assessing oxidative status and essential element levels as the main mechanism of Pb toxicity in the liver and kidneys. Furthermore, dose–response modelling was performed in order to determine the benchmark dose (BMD). Forty-two male Wistar rats were divided into seven groups: one control group, and six groups treated for 28 days with 0.1, 0.5, 1, 3, 7, and 15 mg Pb/kg b.w./day, respectively. Oxidative status parameters (superoxide dismutase activity (SOD), superoxide anion radical (O2−), malondialdehyde (MDA), total sulfhydryl groups (SHG), and advanced oxidation protein products (AOPP)) and Pb, copper (Cu), zinc (Zn), manganese (Mn), and iron (Fe) levels were measured. Lowering Cu levels (BMD: 2.7 ng/kg b.w./day), raising AOPP levels (BMD: 0.25 µg/kg b.w./day) in the liver, and inhibiting SOD (BMD: 1.3 ng/kg b.w./day) in the kidneys appear to be the main mechanisms of Pb toxicity. The lowest BMD was derived for a decrease in Cu levels in liver, indicating that this effect is the most sensitive.