The depth-of-field in a 3D lenticular picture is determined by technological limitations, and cannot be increased by software or image processing alone. However, displayed depth can extend beyond the sharply imaged zone if it is appropriately blurred.
Blurring outside the sharply imaged zone is done by taking an excessively large number of distinct photographs, and then reducing it to a smaller sequence using linear filtering. This process is explained in my book. In principle, there is no limit to the displayed depth of blurred content. However, the blurring increases with the distance from the center of the sharply imaged zone.
The pictures below demonstrate the blurring required to extend the depth display. The left image is the original photograph, and the right image is its blurred version obtained by a linear filtering process. The center of the sharply imaged zone is set to the model face plane, so the face and its vicinity within the depth-of-field remain sharp.
In this example, the total displayed depth is 200mm, and the depth-of-field is 50mm, thus the depth display is enhanced by a factor of 4.