There are several features in Pokemon Sun and Pokemon Moon that give your pokemon additional experience after every battle. The ones that I know about are:
Trade Bonus - Pokemon caught or hatched by another trainer and traded to your game gain 50% more experience than pokemon you caught or hatched yourself.
Refresh Bonus - If your pokemon has two or more hearts in Pokemon Refresh (called Pokémon Amie in Generation 6 games), it will gain 20% more experience.
Lucky Egg bonus - The held item Lucky Egg (which you can get by speaking to Kukui after getting 50 entries in your pokedex or by stealing from wild Chansey) will increase the experience the pokemon holding it receives by 50%
Do any of these have an affect on how much experience a pokemon gains using the Level Boost drink in Poke Pelago?
So I've done my own test on this, and none of the boosts I was interested in - different trainer, Refresh, and Lucky Egg - had any effect. I had four level 1 Littens - one obtained through Wonder Trading, one who had more than 2 heart in Pokemon Refresh, one who was holding a Lucky Egg, and one I used as a control. After subjecting all four Littens to 40+ hours with the Level Up drink, none of the Littens had gained any more experience than the other. All of them were the same level, and even had the same "XP to next level" number. If you want more experience, it looks like you either have to let your pokemon play for more sessions, or just grind for experience the old fashion way.