With the third biggest Wishes in the tier, only behind Alomomola and the fairly irrelevant Wigglytuff, and access to Heal Bell, Lickilicky is arguably the best cleric in NU. While Alomomola has a much higher HP stat and Regenerator, Lickilicky can take on special attackers including Kadabra, Altaria, Gardevoir without Focus Blast, Regice, and more with ease while still taking on physical hits well enough. Similarly, unlike Audino, which has similar support moves, it can hit the foe back with a decently powerful move due to a decent Attack stat, and is also overall more bulky.
Wish is an excellent support move, as it provides Lickilicky with a way to heal 50% of its HP and also a very large portion of its teammates' HP stats, especially those that do not invest in HP, namely offensive Pokemon. Heal Bell clears status away from the team, which means that not only can it save its teammates from an untimely burn or paralyze, but it's also not worn down by Toxic like other defensive Pokemon nearly as easily. Protect ensures that Wish heals Lickilicky, making it much harder for special attackers to get through it. Finally, Body Slam is preferred as the attacking move, as it can do decent amounts of damage and it also has a chance of paralyzing the foe, which can make faster opponents almost useless. Dragon Tail is a usable alternative, as it can phaze the foe while not being affected by Taunt and gives Lickilicky a way to hit Ghost-types. However, be warned that it is less than half as strong as Body Slam, and will fail to break many Substitutes.
While it may seem strange to put Own Tempo over the clearly superior Cloud Nine, Wish and Cloud Nine are incompatible, due to Wish being from a Gen 3 event and Cloud Nine being from the Dream World. Ultimately, Own Tempo is far better than Oblivious, as it at least makes it easily take on the incredibly annoying Liepard, which often runs Swagger. Return is usable over Body Slam or Dragon Tail because it puts a bit more of a sting on foes, but due to its lack of a side effect, the other two moves are more useful from a utility standpoint. If Heal Bell is not needed, both Dragon Tail and Body Slam can be used.
Being a cleric, Lickilicky does not need very much support, and instead usually supports its own team. Wish is useful for practically any Pokemon that lacks instant recovery, such as Regirock and Regice, as it ensures that they will not be worn down as easily. Misdreavus appreciates Wish as well due to its low HP stat and unreliable recovery. In return, Misdreavus can wall Fighting-type Pokemon such as Sawk and Gurdurr, which can otherwise destroy Lickilicky or use it as setup fodder. Offensive Gardevoir is a similar case, and while Sawk tends to do a lot of damage to it thanks to its low physical bulk, it does appreciate Wish healing almost all of its HP and can easily OHKO Fighting-types. Skuntank also makes a good partner, as it can deal with Ghost-types such as Haunter and Misdreavus that Lickilicky can potentially be unable to damage. Skuntank also benefits from Wish and Heal Bell to capitalize on its decent bulk and remove burns, allowing it to perform its role for longer. Finally, if Dragon Tail is used, entry hazard support is helpful to damage the foes as Lickilicky phazes. Pokemon with Spikes, such as Garbodor and Scolipede, make good partners, as both resist Fighting moves and lack instant recovery, meaning Wish will help them out a lot.