Characters that midscreen Throw, LP, Net either doesn't work on or not worth trying:
Shang, Sheeva, Female Ninjas, Sonya, Sindel, Liu Kang and Kung Lao. I would even say don't bother vs Nightwolf and the Robot Ninjas, because they land very close to the ground when it does catch them in air, sometimes, it'll even put the net a little below where it would be if they were standing in the net which can throw off whether you choose to juggle or combo, similar to an air freeze with Sub that actually has them on the ground.
Instead do, LP, JK, then do the air throw as they drop and you will land close to them, and it makes rushing easier. If you don't want to do that, then do a HK after and a drop a bomb as they get up, then start some zoning strats. Regardless of the character, using the air throw as they land on the final hit is generally a good idea because even if it doesn't get you very close, it often baits some special moves that you can then counter, so kara jab right after you land to block the attack and make them confirm by still moving after landing, this results in about a 50% scenario for Cyrax using multiple tactics and options.
After the Throw, LP, Net, you have the option of aaHPHP (aaHP, aaHP on male ninjas) and then air throw or JK generally, or even mid screen, wait to time the jump so they fall out of the net as you connect a deep JK, aaLP or HP, air throw, or JK. If that's too difficult, do, Throw, LP, Net, JK, air throw, which is a bit more than aaHPHP, air throw.
If in the event you actually do get a grounded net after the throw that is either unblockable or just wasn't blocked, Cyrax's full combo with a JPS does less damage than a simple, cross up JK to Air Throw.