LT_execute gets back into LT and the general problem of Active window and Active Layer. so OC provide page and layer level LT_execute so that the LT string passed into those versions of LT_execute can assume that object as the Active window or Acitve layer. This is very much like the LT version of win -o {script} or layer -o {script}.
It is easy to forget all these little problems and hidden assumptions in the LT world once you are more comfortable with OC, where everything is clear by simply looking at the C/C++ code.