You can add a "Lost Reason" Custom Field in the Customize section of Settings. The Lost Reason will only display in the Status section when a Deal or Project is set to the Lost Stage. 

Any Custom Field that starts with a Stage name will appear once that Stage is set. So if you add "Lost" followed by any other words to describe your Custom Field name then it will appear once the Lost Stage is set. 

1.) Tap on More (...) in the lower right of your screen on mobile (iOS/Android) and lower left on 

2.) Tap on Settings


3.) Tap on Customize to expand the section and then scroll down to the Deals (or Projects) section.  Than tap on the gear icon next to the Deal (or Project) Segment to which you would like to add custom fields.

In this example we are going to add Custom Fields to the Default Deals Segment. You can add Custom Fields to each Segment.

4.) Scroll down to create a new Custom Field.

Tap on Add to create additional Custom Fields beyond our default fields.