Ok. Not sure how many names have changed....................
On our previous lightweight (1.2tonnes) fractional rigged 24footer we ran symmetric spinnaker braces and sheets as the same line - so just the one rope from each corner of the kite. Gybing was a breeze till we got more older and softer and demented and hence more uncoordinated when the wind got over 20kts.
Now for our lightweight (2tonnes) fractional rigged 30footer we run kite braces and kite sheets - so 2 ropes off each symm kite corner and we can gybe the pole across in winds up to 30kts and boats speeds up to 12kts as long as the skipper and kite brace / sheet trimmers do what the foredeck crew tell them to do..........which involves listening by the after guard obviously...............they are not usually used to that.........so yes if you want to call the brace on the leeward side which will become the new brace after the gybe then that is the lazy brace.........but the co-ordination of the old and new brace, and old and new sheet, through the gybe is the critical aspect.
So boom topping lift is correct terminology for the mainsail boom.
Kite pole topping lift is the correct terminology for the kite pole.
As for ready about lee ho or ready about gybe ho..............cripes that would confuse Einstein............see discussion here
forums.ybw.com/index.php?threads/going-about-what-commands.240642/To conclude;
Ready about means you are going to tack - nothing else needs to be said.........make sure all the crew are ready and prepared..
Gybe ho means you are going to gybe - nothing else needs to be said..............make sure all the crew are ready and prepared..