LODAs are usually issued to conduct transition training for a specific model of aircraft, e.g. RV, Lancair, etc. It will usually require a training syllabus for that transition training. There are several individuals with LODAs in the RV community spread around the country.
You might find information specific to those at the Vansairforce.com forums.
A CFI can instruct in an E-AB aircraft, no compensation can be charged for the use of an E-AB aircraft.
Ralph