After a long journey through Rock Tunnel, you arrive in Lavender Town.
Explore the Town
When you first arrive in town, there will be a cut scene where a Cubone goes into a building, and your rival follows it.
In the Pokémon Center, there is a woman named Diggette who will give you a level 25 Alolan Diglett if you give her a Diglett.
In the lobby of Pokémon Tower, talk to an elderly woman to get a Formal Set for your Clothing Trunk.
Go up the stairs. Go south past the graves to find a hidden Pearl.
Go west from there to find an Elixir.
Go north to find your rival, who will battle you. Your rival has a level 27 Pidgeotto, a level 27 Gloom, and a level 28 Jolteon or Raichu (Jolteon if you are playing Let's Go Pikachu, Raichu if you are playing Let's Go Eevee). You get 2240 Pokédollars for winning.
Go west from your rival to find an X Attack.
Go south from there, and you can battle Coach Trainer Holly, who has a level 28 Geodude. You get 2800 Pokédollars for winning. After the battle, you get 5 candies for your partner pokémon's species (Eevee Candies if you are playing Let's Go Eevee, Pikachu Candies if you are playing Let's Go Pikachu).
Go up the stairs and there will be a cutscene.
On this floor, ghost pokémon will float around. If one of them touches you, you will be sent back to the lobby of the tower.
At this point, you won't be able to make it all the way to the top of the tower, so just let a ghost send you to the lobby for now.
Outside, go toward the west exit of Lavender Town and you will see Jessie and James. They are going to the Rocket Game Corner in Celadon City, so that is where you should go, too.
Go west from Lavender Town to Route 8.