This is a tip for Lex VS. any champion.
When chasing down your target, don't blindly follow them.
It's best to let them walk into your hands, cut them off around corners.
Line up your crosshair with their head, for an easy headshot.
* Lead the Androxus into a corridor/small space to make your AOE attacks more consistent and reliable. All legendaries are viable, but WYRM jets is your best bet at making him waste his nether steps.
Lead your shots. If you have a projectile, never shoot at her; even in close range you must shoot ahead of her. If you have a hitscan, wait until you have her in your crosshairs to shoot.
If the tip of his arrow shimmers, he is preparing an Impaler Arrow. Avoid being pinned to the wall at all costs; his Planted will do 2400 damage before you can even move again, and likely another 2400 to follow, killing anyone.