NavList:

To be clear: the only time you need to measure the altitudes is very close to the time you measure the lunar distance. One method is to measure the altitudes just before and after the lunar, and interpolate for the altitude at the exact time of the lunar measurement. The purpose is to get the proper refraction, parallax and semi-diameter values in order to correct your lunar measurement.

I think I am starting to understand.........

 LD = arccos[sin(Dec1)*sin(Dec2) + cos(Dec1)*cos(Dec2)*cos(GHA2-GHA1)]   so to for the calculated LDs all you need is Dec and GHA. The GHA can be approximate. You pick a time  consistant with your DR.

The parallax, refraction and SD must be known to clear the measured LD.  This requires an altitude sight close to the time of the  distance measurement. How accurate must the  observed altitude be? Looking at the Air Almanac the P in A is 45' for altitudes between 36° and 38° which suggests that  altitude need be measured only to the nearest degree. This would make the altitude  sight a lot easier.  Of course the NA may give more precise corrections.

Even if you were very unsure of the time, it is not difficult to calculate the distances for each whole hour and compare them to your observation to see which pair your observation lies between. Once you find the hours at which the distance is greater and lesser than your observation, all that is left is to interpolate to find the minutes and seconds.

Very easy for 21st century Lunerians with massive computing power in their pockets but probably  something a pen and paper navigator would avoid.

Descriptions of Lunars I have read seem to concentrate on clearing the distance which to me is a side issue. It is like explaining cellnav by discussing in detail how to correct an observation for refraction, IE and SD without explaining anything about intercepts.