I mentioned lighting or lack of.
Again, lighting or lack thereof has no bearing on establishment of an LPV DA. Approach Lights can decrease the minimum visibility required if they are of the right type. ref: FAAO 8260.3D, Table 3-3-1 and surrounding paragraphs and tables.
I also mentioned a note indicating a Threshold crossing height. TCH is a clue that something is concerning about a RW 13 approach. Sorry, I didn't look any deeper. I got a life. One reply quickly informed us that TCH's were either 40 feet or 60. Well that was the "what" but not the"why".
Having a TCH is NOT a "clue that something is concerning". Most approaches chart a TCH * - it's simply the height above the threshold that the glidepath crosses the threshold at. They're not "either 40 or 60" feet, I said the usual range is 40 - 60 feet. Ref: FAAO 8260.3D, Table 10-1-1.
Why is there a TCH? Well, how high would you like to cross the threshold at? You can't cross it at zero. The touchdown zone markers are 1000 feet down the runway because that's approximately where an airplane on an instrument approach is expected to touch down. At a 3.00 degree glidepath, a 50 ft TCH intersects the runway 954 feet from the threshold. So the typical value is about 40 - 60 feet, dependent on several other factors, one of which is "what is the VGSI set at?"
* TCHs are not charted on circling-aligned approaches, for example, and in some other cases due to what are known as "visual segment obstacles"
I mentioned that lighting, lack of it or other components or other visual aids routinely affects minima. A quick reply directed me to my OPSPECS. I don't have any under 91. That table is in the Jepps or with the procedures.
You stated that a lack of REILS is a factor in determining why 5N8 doesn't have LPV minimums to runway 13. That is not true. Lots of airports have LPV minimums but no REILS. Even if a runway has REILS, their presence alone does not have any effect on either DA or visibility minimums, at least in the U.S. Even a full approach light system has no effect on DA.
You stated that "we check notams in planning to find the inop components & visual aids so we can go to the table to derive our proper minima", in response to my comment about lighting having no effect on the DA. If you are in fact deriving your own (higher) DA based on lighting outages, then what you are doing is above and beyond what Part 91 requires (hence my OpSpec statement). Yes, if there is an approach lighting system installed, and it is out of service, then you may need to increase your visibility requirements using the Inoperative Components table, the Jepp charted values, or the Inoperative note on the chart. But that's visibility, not DA.
All of the posts above have given many good, possible reasons that 5N8 runway 13 does not have LPV. It could range anywhere from "obstacle environment" to "nobody has asked for one to be developed yet". The only way to know for certain is to contact the FAA at the website I linked above. My understanding is that they do respond fairly quickly.