One idea I have is for a restaurant that secretly employs a Lickitung as its chef. This is a closely guarded secret but they do it because his dishes are amazingly delicious and their restaurant has become famous since he started cooking for them. The player will find out about this and through wacky shenanigans be forced to deliver specific ingredients and help around the kitchen. At the end of the side quest, someone finds out about the Lickitung and the restaurant will be closed down by the health inspector. The player will then be offered the chance to catch the Lickitung, because he wants to travel the region in search of more recipes.
On visiting the xxxxx Restaurant in xxxx Town, one of the waiters will recognise you as a trainer and ask for your help. He wants you to find a range of bizarre berries for the new chef, who, it turns out, is a Lickitung.
Some of the waiters are being harassed by the customers who are demanding to find out the secret to their new recipes. Soon, they barge through the door and find Lickitung at the stove. It bolts through the door and away, but you can capture it, as it is hiding behind the restaurant.
Reenter the restaurant a day or more after completing the initial quest.