Further in my Pokemon Crystal playthrough and as you can see it takes me a lot of time to sit and play :P But about the game. For me it always was strange, that after you catch Red Gyarados, you need to talk to Lance and without having an option to decline, you go with him. You going with him to attack Team Rocket hideout... Attack Team Rocket with total stranger... A freaking evil gang probably with weapons and traps... Yeah, you defeat Red Gyarados, but you send your pokemon to attack another pokemon, so it is like animal fighting with another animal. Attacking real bad people could end up with gun wound or death. So my theory for Crystal taking that risk of going with total stranger to attack Team Rocket is like this.
Crystal is a teenager, that is why other people call her kid, but she is old enough to go for a road trip, 'cause her mom allowed her :3 I think she is 16-18 year old to be still called a kid, and it is summer that is why she doesn't need to go to school :3 She is a teen girl, so she probably reads those dreadful novels about sparkling vampires :3 Lance has a cape like Dracula, is an adult and have this mystery look. Probably Crystal when she saw him, got her first crash on someone who looks like her favorite male characters from books and fanfics x3 That is why she is accepting his quest :3
What do you think ;3?

Pokemon team now:
Marowak - Bonehead (before Bonnie)
Feraligatr - Sunshine
Arcanine - Robert (before Bobby)
Golduck - Don Juan
Eevee - Richie

Art @  Razor-The-Cross-Fox

Pokemon @ Game Freak