op says wrote:
He asked if he could go to any LT tire as long as they had the correct load carrying capability.
Most LT tire manufacturers have several lines of LT tires. I've found most will recommend one or two of their LT tire lines for trailer use and may not recommend other lines. Stick with a AS (all season) type tread.
These 16" LT E tires have been recommenced by their manufacturers for trailer use;
Michelin XPS Ribs
Bridgestone R250
Firestone Transport HT
Uniroyal HD-H
BFG Commercial HT
Cooper SRM II
Goodyear Wrangler HT
These are tires with proven track records on all types of trailers from RVs to commercial type trailers.
Be careful of low cost off shore brand LT tires if the trailer is going to be on the road for thousands of miles at interstate speeds.