The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument was launched as part of the Lunar Reconnaissance Orbiter (LRO) spacecraft in June 2009. Its purpose is to measure the linear energy transfer (LET) spectrum in lunar orbit as an aid in determining risks to human crews on future lunar missions. Part of the preparations for the mission involved estimating the LET spectrum for the anticipated environment that the instrument is likely to see during the 1 year operational phase of the LRO mission. Detailed estimates of LET spectra in the six silicon detectors and two tissue equivalent plastic segments were made using the beta version of the HETC-HEDS Monte Carlo transport code. Tables of LET in each detector component, for incident particle elemental species from hydrogen through iron, were carried out at incident particle energies from 20 MeV per nucleon to 3 GeV per nucleon. The LET values in these tables have been parameterized by elemental species and energy for ease in quickly and accurately estimating the LET response for any input solar or galactic cosmic ray spectrum likely to be encountered during the lifetime of the instrument. The parameterized LET values are in excellent agreement with the HETC-HEDS calculations. Typical differences are on the order of a few percent. These parameterizations will also be useful in validation studies of the Earth-Moon-Mars Radiation Environment Module using CRaTER measurements in lunar orbit.