Always try to find weapons with good accuracy/firerate - so even if you mess up the first shot, you'll have a good enough chance to hit with your next before you get hit. Most pistols work well (except for AuG and Magnum of course), RCP 90 is easymode. Just don't try to use the DK5 too much as well as the shotguns - long distance shots hitting your target 100% with them are nearly impossible. You even might use proximity mines, but stay away from the other mines, also from grenades and the grenade/rocket launchers bear a high risk of killing oneself in LTK.
And shoot whenever you see a single pixel of your enemy, even if he's running away unknowing you're behind him chances are you'll lose him or he turns around before you get a chance to kill him, so giving away your position isn't that much of a deal.
Next keyword is: bullet penetration. Learn which weapon can penetrate what and use it to your advantage - doors, windows, everything might be useful. (also the sound of a door opening will help - he'll likely pass through it a moment later -> in Facility there's two doors in a row, you might hear him and shoot through yours)
And last but not least: weapon/ammo pickup sounds, weapon/ammo spawns. If you're just two people on the map you'll always know when you hear the sound that he's nearby, when you don't see the supply where it should be that he passed this spot. You might also want to try and avoid picking up ammo yourself if you have enough (and in LTK that's usually after picking up the weapon + max 1 ammo crate), hiding your trails.
Shooting at random to lure him to you should only be used when you're confident in yourself.