Close Combat has perfect accuracy and 120 base power, which is more than Cross Chop. Lucario is going to take damage that will KO it anyways thanks to Ground and Fighting weakness combined with the power behind the Pokemon in OU and weak defenses for OU. Close Combat gives Lucario a much better chance of taking down these foes before they can take it down.
Here's a quote to how good Close Combat is, you'll miss out on this with Cross Chop:
Even Skarmory is almost always OHKOed by a +2 Close Combat after
So I would also tack on Swords Dance over Me First. It would also be a good idea to slap on Extremespeed and Crunch in place of Drain Punch and Counter.
That above was the competitive answer. For the ingame answer, you'll still best be using Close Combat for the sheer power of the attack, plus the fact that it has perfect accuracy. The defense drops are of no consequence when you KO everything the foe has.
As for the rest of your moves for ingame (not part of the question, just want to help) you'll want to replace Counter and Me First. Ice Punch (if you have access to Move Tutor), Thunderpunch (same as Ice Punch), Rock Slide, or Earthquake are better options.