If she's any sort of a typical player, Gengar's fourth move is most likely hidden power, probably ice, and lucario's fourth would be crunch.
You basically know my Pokemon by this point, but I can re-post the list from MP if you want.
While her team doesn't have any obvious weaknesses, and maybe I'm just thinking this way because I'm used to using it, but I think my rain dance team probably could beat her.
Crobat is fast enough to Taunt Azelf out of Stealth Rock, if you want to teach it that, or else Rain Dance will protect from Fire Blast, and can U-turn to Bronzong or Rotom to block Explosion... Although you can't use Rotom in Wi-Fi, can you...
Additionally, Crobat's U-Turn will break Celebii's Leech Seed, dish some serious damage with the double weakness, and with Rain, it's effectively resistant to both Celebii's attacks. Taunt would also stop Recover.
Gyarados will keel over from a thunder from either Starmie or Rotom, and Starmie can spin away Azelf's rocks. With Rain-boosted Hydro Pump, Starmie should also be able to take out Gengar, Lucario and Tyranitar.
Rotom's Trick can effectively shut down Lucario, Celebii or Azelf if used right, and it can still hit the later two for a weakness, and remain reasonably safe from their attacks.
Sharpedo may not function so smoothly without its Choice Band, but a rain-boosted Aqua Jet still might be able to take out Gengar, while Crunch can still hit Azelf and Celebii, Earthquake for Lucario and Tyranitar...
Kingdra's speed is doubled in the rain, allowing it to easily take out Tyranitar, Gengar and Lucario. If it can beat Gyarados to the dance, Outrage might be enough to down it, and Celebii as well.
Bronzong acts as general support for the team, including hypnosis, stealth rock and rain dance...
In the end, while Rotom, Sharpedo and possibly Bronzong may not be the best choices for this battle, with Crobat, Starmie and Kingdra, you already have three rain dancers and a good and likely hit against everything on her team.