SCALES is a new instrument that will be mounted on the Keck 2 Telescope just downstream of the Keck 2 AO system. SCALES is designed to take spectra of directly imaged exoplanets at multiple wavelengths in the thermal infrared (1-5 microns). The ability to switch from science imaging mode to pupil imaging mode to taking spectra for specific wavelengths requires precision mechanical subsystems to enable these different modes of operation at cryogenic temperatures (-200C). In this paper we discuss the design of a rotary stage that can position different Lyot masks, as well as different high precision metal optics to enable some of the broad functionality of SCALES. Henceforth we will refer to this rotary stage as the Lyot mechanism. We will also discuss the design and analysis of the optics mounted to the Lyot mechanism, as well as thermal analysis and testing of the stepper motor drive system.