Following an RV Forum on trailers.
If you change from LR-D to LR-E (or from LR-C to LR-D) you will only get an increase in load capacity, or an increase in the Reserve Load,
if you run higher than the Certification Sticker inflation psi. If you
look at the Load & Inflation tables (they are almost all identical
for ST and LT type tires) and look at your actual scale weights you can
calculate your current Reserve Load and see what inflation you would
need to get to a Reserve closer to 20% or 25%. Due to the unique forces
("Interply Shear") tires
must tolerate on multi-axle trailers, I and other tire engineers suggest
at least a 15% Reserve with 20% being better. On my personal RV I run
20 to 25% Reserve Load.
While we are talking about the certification label, I advise people to snap a picture of the label, or labels if more than one, along with a shot of the complete tire size and Load Range info on your tires PLUS the full DOT serial including the data code portion of the DOT serial. That way if the printing on the sticker fades or your tire gets cut and destroys itself you have a record so you can file a claim if you purchased "Road Hazard" warranty on your tires as I have, or need to check against a tire recall notice, you can answer the question of what size and Load Range you are currently running. Keep a picture of the Weight Slip too. Its a lot easier to have all this tire related info in one place on your phone.