The short answer
Gerson used the right side to encourage broader distribution within the colon.
The basic Gerson method directs the person to lie on the right side with both legs drawn toward the abdomen and to breathe deeply. Gerson’s stated aim was to help draw the greatest amount of fluid into all parts of the colon.
The plain-language anatomy
The colon curves from the rectum around the abdomen. Position and gravity may help the solution move through those curves rather than simply pooling in the lowest area. Drawing the knees up and breathing slowly may also help the abdomen relax.
That practical rationale should not be inflated into a claim that the position has been proven superior for every outcome in a modern comparison trial. It is the historical Gerson direction used in the basic method described in the book.
The coffee doesn’t travel directly to the liver
The liquid stays inside the bowel until it is released. The proposed liver connection concerns compounds absorbed through the bowel wall into venous circulation. Blood from multiple parts of the large bowel drains toward the portal circulation and liver.
A complete modern human coffee-enema study has not directly measured every step of the proposed detoxification pathway. Rectal caffeine absorption itself has been demonstrated in a small randomized crossover study.
Human absorption study