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?