The stock header is only 1.3" ID which is minimally adequate for a totally stock engine.
Replacing the stock muffler with one that flows better, even just a HD unit, will require a little rejet and tune, but will improve efficiency and add a little power.
Going the next step by replacing the stock cam with a Stage 1 Performance cam improves air flow such that replacing the stock header with one that has 1.5" ID will dramatically improve air flow and engine efficiency throughout the entire rpm range, with the most improvement in the midrange.
Thiis would of course require a reject/tune of the stock carb, or if you want an even better boost in overall efficiency/power then replacing the stock carb with one designed for performance will add even more efficiency & power.
The next step up, if you want to go there, is a larger piston.
They come in 95, 96 & 97 mm with an increase in compression ratio. Even here there is a choice of near stock CR or jump to a 10.5:1 CR. Do that and a 1.65 ID pipe (1.75" OD) will Jack performance even more.
I do recommend that when boring the cylinder for a larger piston the cylinder should have the silicone carbide treatment be done. It will reduce friction; reduce heat as a result and make a bit more power available; reduce possible seizure if you run low on oil; and increase cylinder life dramatically.
If I had just one mod to do to an engine it would be the silicone carbide treatment for the cylinder?
The 1.65" ID pipe is the most needed for this engine when used on a street bike. If you build a racing engine, though unlikely for the LS650, then perhaps something larger might be considered but that is way above in our normal daily functioning bikes.