Since any Pokémon can hold a Lum Berry, the only thing we need to find is which Pokémon learn Rest and Recycle. And as it turns out, A lot of Pokémon get this combo:
Abra and evolutions
Arceus
Azelf
Baltoy and evolutions
Braixen and Delphox, but not Fennekin
Bronzor and evolutions
Bunnelby and evolutions
Chingling and evolution
Cleffa and evolutions
Cresselia
Dedenne
Delibird
Deoxys (all forms)
Drifloon and evolution
Drowzee and evolution
Elgyem and evolution
Espurr and evolution(s)
Genesect
Girafarig
Gothita and evolutions
Happiny and evolutions
Heatmor
Hoopa (both forms)
Hoothoot and evolution
Igglybuff and evolutions
Jirachi
Kecleon
Klefki
Klink and evolutions
Lunatone
Magnemite and evolutions
Meditite and evolution
Meloetta (both forms)
Mesprit
Mew
Mewtwo
Mime Jr. and evolution
Munchlax and evolution
Panpour and evolution
Pansage and evolution
Pansear and evolution
Porygon and evolutions
Ralts and evolutions
Slowpoke and evolutions
Smoochum and evolution
Solrock
Spinda
Spoink and evolution
Staryu and evolution
Trubbish and evolution
Uxie
Source
