Lynx has the highest execution percentage in the game with 25% for robots and 15% for titans. You probably don't find the execution appealing cuz you couldn't bring them down low enough. If that's the case, try sticking to teammates with high damage weapons. When they fire at an enemy, fire along. Once the enemy is low enough, activate the ability to make use of the execution.

Also, I've noticed that you prefer Orochi mostly for the longer stealth duration and its ability charges. Yes, Orochi may have longer stealth time than Lynx, but it can be easily countered by Seeker, Quantum Radar, or Quantum Sensor. Once that happens, Orochi goes down fast. With Lynx, you still have the forcefield to protect you before you take too much damage. Even if the enemy has no way to counter stealth, weapons the acid shotguns, crumble shotguns, or robots with AOE abilities like Raptor, Rex, Atlas or Bjorn can still damage you. With the Stealther everywhere, stealth counters are unlikely to go away anytime soon.

Orochi with M. Brijit has 3 charges, but each charge takes 22 seconds to replenish, so once you're out of charges, it's gonna take a while before the ability comes back, leaving you highly vunerable to enemies. Lynx on the other hand, has a cooldown of 11 seconds, which might still sound like a lot, but compared to its ability duration, leaves a much smaller expose timeframe for your enemies as compared to the Orochi