Lickylicky probably won't be facing the weather starters unless you can make them come in, and that means changing the weather yourself with Lickylicky.
Lickylicky@ Expert Belt/ Leftovers
Cloud Nine
Careful
100 HP/ 252 Att/ 156 SpD
Sandstorm/ Sunny Day/ Rain Dance
Power Whip
Earthquake
Toxic/ Brick Break/ Explosion/ filler
Lickylicky is pretty bulky and is very capable of taking a hit, so coming on after a KO or switching in on a set up turn or attack should be pretty simply, especially a special hit considering the EVs. Sandstorm is the primary option because I feel that Sun and Rain are harder to counter than Sand, and EQ and Power Whip hit most common Sand team Pokemon pretty hard anyway. Setting up Sandstorm in either the Rain or Sun will draw out Politoed or Ninetails, and since you know which one will be coming out you choose either Power Whip or Earthquake to hit for SE damage and likely get a OHKO with SR support. The EVs are designed to take hits from Toed and Tails because both of them are specially based, and without boosts from the weather, they won't be OHKOing Licky.
I'm not really sure what to do with the last slot though. If you have more trouble with sand, the set could easily be made to be specially offensive and carry Surf and Focus Blast (or mixed with Brick Break I guess) and physically defensive to be able to take hits from the usual sand threats. Obviously you would want to use Sunny Day or Rain Dance instead of Sandstorm as well.
Thoughts?
Well, if you did want to you should probably put the weather rocks on there. I still don't get why explosion's so good, I mean it still gets stab but since it's not going to OHKO nearly as awesomely as it did in 4 why would anyone use it over another SE move that could catch something else and do the same thing.
I also don't get why this thing has to set up weather, I mean, I understand luring them out but they're just gonna try to kill Licky because they know you're going to hammer them for SE. And Licky really can't use any of the weather effects either. I'd rather use a fast weather inducer (electrode!)
I figure Licky's job is just to counter the sweepers and the inducers, or one or the other if you want it to. It can tank and somehow with a scarf it *does* outspeed Exca and all the other sweepers.
But I do like the idea of Licky resetting the weather. (I love it) I mean, that might be reason enough to just use a random one on it. "Hey sandstorm teams. I know you like sand and all... but bam! It's raining now. Sorry Exca!" Even if it doesn't lure in the weather starters it would do a great job of messing with the teams without being on a weather team yourself xD.
tl;dr It's doing too many things at once. Good idea, but I dunno if it'd work in practice.
I know this is a sketchy idea, perhaps. But, perhaps lickilicky can take advantage of its bulk, and invest some EV's into sp.def and defense, but also have curse? Then be a physical attacker with great defenses. With the elemental punches from Gen 4, Earthquake, Rock Slide, and Power Whip in its physical movepool, seems like an amazing tank.
Well yeah, but it does lose Cloud 9 if you use the ele punches =\. And in a weather based game cloud nine's it's best selling point. But yeah it would make a great tank. Like an anti meta tank xD