This is a response/expansion to a post written about gynandromorphy by a student in my developmental biology class, Miles. It may be useful to read this post prior to reading the following post.
Gynandromorphy occurs when an organism displays both female (gyne) and male (andro) physical characteristics (morph) due to sexual dimorphism. In the photo of the gynandromorph lobster, it appears as though it is bilaterally symmetrical. However, this is not always the case. In fact, some gynandromorph organisms display a mosaic pattern in which the two sexes are not differentiated as clearly. The pattern of gynandromorphy is dependent on the determination pattern of cells during division. This disorder is a result of an early event in development, specifically mitosis, which does not split the sex chromosomes in a typical manner. Although I was curious as to whether these organisms can reproduce, I couldn't find any information on the topic. However, many articles related this disorder to hermaphrodites and intersex individuals of the human species. In these cases, most individuals are sterile as a result of their disorder. With most individuals, the reproductive organs are incomplete and can, therefore, not reproduce. It may be possible that an individual with gynandromorphy or hermaphroditism with complete organs could reproduce but I do not know nearly enough about the subject to speculate.