The mass replay checker, to improve speed, temporarily disables the flushing of loaded pieces (basically - NeoLemmix usually keeps any graphic set it loads in memory, but will discard any that haven't been used for a while; during a mass replay check, this discarding is turned off). Removing the code that disables this causes it to run the check on Reunion with no issues.
So - the next thing to figure out - is it that something isn't working properly when the discarding is disabled, or is it just that Lemmings Reunion is loading so many pieces that it reaches some kind of limit? The latter is possible - Lemmings Reunion uses a lot of graphic sets, and if I'm not mistaken, in particular, it still uses the "Epic" set instead of proper mixing. Some sets might also still be at Lemmini resolution internally, which could also potentially cause issues (though if they do, this needs to be fixed on NL's side anyway). Such graphic sets can be fixed by loading and re-saving them in a recent version of GSTool; this will hard-resize them to NL resolution.