The field doesn’t look like it is a droplist either, so I suspect that something in the setup is broken?
NewForm and EditForm are different forms and can have completely different setups. Are both using DFFS or both using JQuery / JS-Utility? Usually SPJS-Lookup will give pretty good error logging (on top of the form) once it has access to JQuery.
I have fixed this plugin so that loading a record in EditForm with a custom value that is not a valid option in the list – with the setting “addYouOwnValue” set to true – will show the field as if you have hit the “Write your own value”.