Teeter Dance isnt poison or illusions its mind manip, and infatuation in pokemon in general has shown to work on human trainers. And regardless of what he tries to do to attack her, Infatuation makes it so the opponent is physically incapable of attacking half the time even if they want to.
Lopunny's evasiveness and combat mobility is insane, and coupled with a huge speed amp from Agility and she'll have no trouble maneuvering through whatever he tries to throw at her. Since this is Mega Lopunny, her entire combat mindset is that of a focused and strategic fighter, to the point that she is physically altered to be more suited to actual combat and even her type changes to that of a Fighting type.
As for CQC stuff, Lopunny actually has two things that will be extremely detrimental to Hibari. The first is Mirror Coat, which will reflect the majority of his abilities back at him dealing double the damage. The second is the IQ skill Counter Hitter, if Hibari lands a solid hit on Lopunny, 1/4th of the damage immediately gets reflected back onto him. Couple this with something like Encore, which will lock him out of being able to use all but one of his abilities at any given time and he's in serious trouble. Lopunny also has stuff like Practice Swinger, which boosts her attack power if she misses an attack, and Quick Striker and Extra Striker, which allows her to attack at a much faster rate.
Lopunny also has the chance to burn Hibari and cut all of his physical power in half with Fire Punch, freeze him solid with Ice Punch, or paralyze him and cut his speed in half with Thunderpunch.
Lopunny also has moves like Charm/Baby Doll Eyes, Fake Tears, Agility, and Defense Curl/Cosmic Power which severely lower the opponent's AP, lowers the opponent's defense, severely increase her Speed, and increases her defense respectively. Also if she lands a single Sweet Kiss or Dizzy Punch Hibari will be double whammy confused and infatuated at the same time.