Alternaria rot, also called black rot or navel rot, is caused by the fungus Alternaria.  It is most common in navel oranges, minneola and Orlando tangelos, and occasionally in lemons and limes. The fungus grows on dead citrus tissue during wet weather. It produces airborne spores which can land and grow on the blossom end of the fruit. Premature fruit coloring and fruit drop are commonly associated with infection. 

Diseased fruits may have a brown to blackish discoloration that is usually at the "blossom" end but may occasionally occur on the stem end as it does in navel orange (photo 1). However, the rot is not always evident on the outside of the fruit. Eventually (frequently not until after harvest) a dark slightly sunken spot appears. This rotten spot may eventually cover as much as one-fourth of the fruit (photo 2). The tips of several segments show a dark rot, and the juice of the entire fruit has an unpleasant taste. Because lemons are frost sensitive, Alternaria rot is often associated with cold damage. Frost damaged tissue is more likely to be infected (photo 3). The rot inside the fruit may not be evident from the outside.

Healthy fruits from well cared-for trees are more resistant to the pathogen. Good cultural practices, proper maintenance, irrigation and fertilization will minimize disease. It is especially important to prevent damage to fruit and splitting since wounds give the fungus a good place to enter. Remove infected fruits and dispose of them by bagging and removing from the site.

Links:
http://cals.arizona.edu/maricopa/garden/html/t-tips/diseases/altrnria.htm
http://cals.arizona.edu/pubs/diseases/az1154/#alter
http://www.ipm.ucdavis.edu/PMG/r107100811.html

Other images:
http://cals.arizona.edu/maricopa/garden/graphic/diseases/limes-alternaria.jpg
http://www.ipm.ucdavis.edu/PMG/A/D-CI-ACIT-FR.001.html