Lex have more damage, but androxus wins on mobility.
Try to strafe/dash in between shots, and use your Q on his RightClick and you should win.
This is a skill match up.
If RMB, you Reversal. Reversal will reduce Lex to low HP. You should always pick the Dark Stalker card. A good way to counter him Is to just out-damage him. You survive more shots than he.
Use Pursuit only when the enemy is low on health since it doesn't do as much damage and if you don't kill them with it you could possibly die,since you are vulnerable and aren't doing as much damage to kill them.
Use your Retribution to reveal the enemy Androxus(or the other Flank champion),it will be easier to win a 1v1 with reveal advantage,you can also give an information to your team about who lurking behind the backline