Mienshao has higher attack (125 to 110) and higher speed (105 to 90). Mienshao has 2 weaknesses, while Lucario has 3.
I <3 Mienshao. It was my first EV Trained Pokemon. Try this:
___

OmniPwnage
Mienshao (M) @ Flyng Gem
Nature: Adamant (+Atk, -SpAtk)
Trait: Regenerator
EV Spread:
252 Atk
252 Speed
4 HP
- Hi Jump Kick
- Acrobatics
- U-Turn/ Swords Dance
- Brick Break/ Stone Edge
(Bold Italics = what i would choose as my moveset
___
Lucario does beat Mienshao at one thing: Lucario can be an awesome MIXED attacker.

Iron Heart
Lucario (M) @ Focus Sash or Salac Berry
Nature: Lonely (+Atk, -Def) or Naughty (+Atk, -SpDef)
Trait: Inner Focus or Steadfast (your choice)
EV Spread:
121 Atk
137 SpAtk
252 Speed
- Work Up
- Dark Pulse/ Flash Cannon/ Hidden Power [Water]
- ExtremeSpeed/ Vacuum Wave
- Close Combat/ Hi-Jump Kick/ Aura Sphere
(Bold Italics = what i would choose as my moveset)
___
\m/o_o\m/