The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) is an energetic particle detector flying aboard the Lunar Reconnaissance Orbiter. Since arriving at the Moon in 2009, CRaTER has observed the deep solar minimum of solar cycle 23, the ascending phase of cycle 24, the very weak maximum of cycle 24, and in recent months, what appears to be the start of the descending phase of cycle 24. In earlier work, we presented lineal energy spectra of galactic cosmic rays (GCRs) at solar minimum for different shielding depths. The long period of CRaTER observations allows us to study the evolution of these spectra as a function of solar modulation. As solar modulation increases, the total flux of GCRs decreases, and lower‐energy ions are preferentially removed from the spectrum of ions that arrive in the inner heliosphere. These effects lead to modest variations in the lineal energy spectrum as a function of time. GCR fluxes at the 2009/2010 solar minimum were high by historical standards and at solar maximum remained high compared to earlier maxima.