The Lunar Reconnaissance Orbiter (LRO) launched on June 16, 2009 has six experiments including of the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) onboard. The CRaTER instrument characterizes the radiation environment to be experienced by humans during future lunar missions. The CRaTER instrument measures the effects of ionizing energy loss in matter specifically in silicon solid-state detectors due to penetrating solar energetic protons (SEP) and galactic cosmic rays (GCRs) after interactions with tissue-equivalent plastic (TEP), a synthetic analog of human tissue. The CRaTER instrument houses a compact and highly precise microdosimeter. It measures dose rates below one micro-Rad/sec in silicon in lunar radiation environment. Forbush decrease (FD) event is the sudden decrease of GCR flux. We use the data of cosmic ray and dose rates observed by the CRaTER instrument. We also use the CME list of STEREO SECCHI inner, outer coronagraph and the interplanetary CME data of the ACE/MAG instrument.We examine the origins and the characteristics of the FD-like events in lunar radiation environment. We also compare these events with the FD events on the Earth. We find that whenever the FD events are recorded at ground Neutron Monitor stations, the FD-like events also occur on the lunar environments. The flux variation amplitude of FD-like events on the Moon is approximately two times larger than that of FD events on the Earth. We compare time profiles of GCR flux with of the dose rate of FD-like events in the lunar environment. We figure out that the distinct FD-like events correspond to dose rate events in the CRaTER on lunar environment during the event period.