The Lightweight Asymmetry and Magnetism Probe (LAMP) is a micro-satellite mission concept dedicated for astronomical X-ray polarimetry and is currently under early phase study. It consists of segmented paraboloidal multilayer mirrors with a collecting area of about 1300 cm^2 to reflect and focus 250 eV X-rays, which will be detected by position sensitive detectors at the focal plane. The primary targets of LAMP include the thermal emission from the surface of pulsars and synchrotron emission produced by relativistic jets in blazars. With the expected sensitivity, it will allow us to detect polarization or place a tight upper limit for about 10 pulsars and 20 blazars. In addition to measuring magnetic structures in these objects, LAMP will also enable us to discover bare quark stars if they exist, whose thermal emission is expected to be zero polarized, while the thermal emission from neutron stars is believed to be highly polarized due to plasma polarization and the quantum electrodynamics (QED) effect. Here we present an overview of the mission concept, its science objectives and simulated observational results.