Level 100 Statistics (see level 5, 50, 100)
Luvdisc has no use outside of NU, and even then, it's inferior to just about any Pokemon. This is quite possibly the most underpowered Pokemon aside from Ditto and maybe Unown (at least Unown has decent attacking stats and is immune to Ground). It lacks the stats and movepool to hurt anything.
With Blizzard, Luvdisc OHKOes Salamence; Ice Beam does 99% max... Rain Dance up against something like Rhydon that won't survive a Surf and hit everything "hard" with Surf and Blizzard. If you come across a Water-type, hit it with Hidden Power Grass. Lum Berry is more useful than Leftovers because, if Luvdisc get statused, it basically loses instantly and everything will either OHKO it or do 90% or so anyway so Leftovers aren't really that important. Even Suicune 2HKOes with Surf in the rain.
Yeah, Luvdisc is pretty bad and has like NO moves. It doesn't even learn Hydro Pump. Flail on a physical attacker is an option (because Luvdisc's Attack is nearly as good as its Special Attack).
Just HP, a defense, and Special Attack for the Rain Dancing Luvdisc. With a ton of Defense EVs, it can survive Choice Band Metagross's Meteor Mash and possibly 2HKO with Rain Dance-boosted Surf.
Checks and Counters
Anything with an attack; look out for bulky Water-types!