The TV coordinate system is defined to be a conventional Cartesian coordinate system (i.e., origin at bottom left-hand corner) referred to the guider display. The transformation from TV coordinates to pointing origin coordinates consists of an optional Y flip followed by a rotation. Given that the pointing origin Y axis is always parallel to the TV Y axis, the rotation angle is always either 0 or 180 deg ( See Telescope coordinate systems looking towards sky (excludes Nasmyth foci) illustrates an arbitrary angle in order to reduce confusion in drawing and labeling axes).
LRIS has two guiders, which happen to be very nearly parallel to each other. The slit-viewing guider is used for defining the TV coordinate system (and we have not yet accurately measured the moveable guider's orientation).
Note that there is a difference between Keck I and Keck II here. The details are not important but Keck I TV angles are 180 deg different from Keck II ones.