Androxus can deflect Lex's In Pursuit ability, also Androxus shoots faster making him more forgiving for missed shots. Although Lex deals more burst damage. This match up is based on whomever goes first.
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