Shortly:
The Lacerta Field Flattener (LFF) performs several tasks:
A lens has a concavely curved image shell, the strength of the curvature essentially depends on the focal length. The shorter the focal length, the more the image shell is curved and the harder the flattener has to work to get it flat. This is done by setting the correct working distance from the flattener to the camera sensor. Lenses with standard design only show a round star image in the center of the image - the further away from the center, the more distorted the stars ("off-axis astigmatism"). Both problems must be corrected by the flattener to produce round stars across the field.
The working distance can - due to different optical designs (ED-Duplet, Triplet, Fluorite-APO, etc.) - deviate slightly from the values given on the flattener housing. Apochromats, which in the optical design have more off-axis coma than astigmatism, cannot be completely corrected (e.g. some Kunming apos with lanthanum glass).
Tested with: Skywatcher EvoLux 62 ED, Lacerta ED 72/432 (and similar), Skywatcher ED 80/600, Sharpstar 107/700, Takahashi TSA 120.