Mostly, I think you'll have to remember the bottom line - that pokémon is a video game. But if we're going to try and make it more realistic, I'd say that pokémon are more durable than humans yeah. And that people probably aren't eating pokémon. In some pokémon universes, like some mangas and even the TCG, animals co-exist with pokémon in the wild, so meat probably comes from them. BUT, is it really much different from when we eat animals? We eat cows but not dogs - similarly pokémon world people could eat Miltank but not Lillipup?
(Let the records state that I know Pokémon is a video game)
Technically, nobody ever said you
couldn't eat Lilipup, or dogs for that matter. In fact, do we even have the liberty to say that Lilipup is the equivalent to the domesticated dog? Sure, it looks like it but we have no idea whether any other similarities exist. Lilipup is no more common a pet than any other Pokémon, to my knowledge. Nor do we have any implications that Lilipup are revered in the same way as dogs, as in our world, we see dogs as friends and pets (in my region of the world, that is) and such is why, or at least one of the reasons why, eating one seems so... uncivil, I suppose. That, and, once again to my knowledge, cows are a better source of food than dogs. (Especially because they are often raised on farms in order to be eaten.) So, perhaps in a Pokémon world that is in times similar to my own, perhaps they raise certain Pokémon for food, Miltank, for instance. Therefore, eating other Pokémon may simply seem unnecessary. However, I don't think that eating a Lilipup would be looked down upon, no more so than eating any other Pokémon that isn't normally eaten. However, I don't know the social standards imposed on the Pokémon world, therefore I don't know what people in that world would be conditioned to believe what is "okay" and "not okay".
But this is all trivial, and barely passes for entertaining conversation.