You need it to teach Rollout and it'll evolve. If remembered and not evolved, level it up once. If forgotten go to where you can remember all your moves that Lickitung had forgotten and then level it up.
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At level 33 Lickitung learns Rollout. That move is required for it to evolve into Lickilicky, eventually at level up, it should evolve into Lickilicky.
In SoulSilver, Lickitung will evolve into Lickilicky once it levels up while it knows the Rollout move. In SoulSilver, Lickitung learns Rollout at Level 33.
Lickitung evolves into Lickilicky when it learns Rollout at level 33.
You can't on leafgreen.
To evolve Lickitung, you'll have to teach it Rollout, and level it up. It will then evolve into Lickilicky.