When sorting fruit that have green or blue mold you should do this activity AWAY from any other citrus, preferably downwind and outside (which I know is not very practical).  At least avoid doing this activity by any air intake into your coolers.  I would place the waste fruit in garbage bags, seal them and discard.  I would not empty loose fruit into your waste container.  The act of dumping the fruit will release millions of spores into the air.  Also when you sort the fruit wear gloves to minimize wounding any of the fruit. These two pathogens are wound pathogens and therefore careful handling is essential.

Whether you need to wash the fruit or not depends on how you plan to utilize the sound fruit.  See below for comments on how lemon storage facilities deal with sporulation.

In lemon houses which store fruit they can have problems with blue/green mold. The storage crates containing mold are dumped in a separate area, following the same general guidelines as mentioned above. When the fruit are dumped they are spray-rinsed with a chlorinated (you will have to find an organic substitute) spray.  This spray makes it more difficult for the spores to become airborne and the chlorinated water will help to disinfest the fruit surface.  They are washed and then rewaxed.  And yes, pack back the fruit into clean cartons.  Discard the soiled cartons.

If you have the space you could: 1) remove the decayed fruit; 2) ease the soiled fruit into a light detergent wash and rinse the fruit.  At this point you can inspect the fruit to see if any lesions were missed when you sorted to remove the decayed fruit; 3) dry thoroughly.  I assume you do not have the facilities to rewax the fruit so I would pack the fruit into clean cartons or bag them and market IMMEDIATELY.

                                                            -Mary Lu Arpaia