I revised and edited it for you. Take it or leave it, these are just my suggestions:
Lyra: (walks on-stage) Come on, Pikachu!
Pikachu: (walks in, panting) Yeah yeah, YOU try keeping up with your speedy shoes...
Lyra: Woah! Since when can you talk?
Pikachu: Uh... Pika pi?
Lyra: (examines mouth)
Pikachu: (bites at fingers)
Lyra: Well! I guess we should go challenge the gym leader now!
Pikachu: Wait, how did you even get me as your starter anyway?
Lyra: the internet!
(Sign: ONE -EASY- BATTLE LATER)
Lyra: Yay! We won!
Pikachu: What are you even doing here, anyway? Last time, I swear you had blue hair.
Lyra: Omigod! Look! It's Team Rocket!!!
(Sign: ONE EASY ROCKET BATTLE LATER)
Lyra: Wow, that was totally easy! Their new pink hair doesn't scare me at all!
Pikachu: (exhausted from battle) You're tellin me...
Lyra: So! Pikachu! How are you?
Pikachu: ... I'm fine
(Lyra starts to walk, Pikachu in tow)
Lyra: So! Pikachu! How are you?!
Pikachu: Did I not just tell you?
Lyra: I JUST WANTED TO MAKE SURE!
Pikachu: Well, stop asking me. I'm fine.
Lyra: Okay. Now, to Azalea Town!
(begins to walk, with Pikachu following)
Lyra: Hey! Pikachu! I just wanted to make sure, are you...
Pikachu: Still fine.
Lyra: Okay, good! I just...you look so cute following me!
Pikachu: Please. The last thing I need is another fangirl on my (bolt-shaped) tail.
Lyra: ...Hey Pikachu?
Lyra: Since when can you talk?
Lyra: Oh, okay! Well, to the next gym!
Pikachu: Why aren't you catching any other Pokemon, anyway?
Lyra: LET'S GO! (grabs Pikachu and runs)
(walks near a Trainer)
Trainer: HEY! Let's battle! I'm not giving you a choice!
Lyra: Oh no! I hope I'm prepared!
Trainer: GO! Piplup! (throws giant Piplup plush)
Lyra: What...IS that!?
Trainer: I just told you, a Piplup!
Lyra: Look, I don't have the National Pokedex yet. And even if I DID, that thing definitely looks like a reject Digimon!
Trainer: Hey! Don't insult him! Go, Piplup! Use your Water Gun!
(nothing happens, obviously)
Lyra: Pikachu! Use your tackle attack!
Pikachu: (kicks Piplup offstage)
Lyra: YAY! We win!!
Trainer: (sulks off in defeat)
Lyra: Pikachu, let's go!
Pikachu: You know, I'm kinda tired...can I at least get a Potion or something...?
Lyra: LET'S GO!
(drags Pikachu away)
(Sign: SEVEN BADGES LATER)
Lyra: (panting) Woah! I can't BELIEVE we just defeated eight Gym leaders.
Pikachu: ...(panting) It's strange...I still feel like I'm at level 5...
Lyra: (blank stare)
Pikachu: And it's amazing how you managed to get all those badges...in a matter of seconds.
Pikachu: ...those aren't really your badges, are they?
Pikachu: That trainer we just beat...you stole his badges, didn't you?
Lyra: …........................maybe. (grins sheepishly)
Pikachu: Really...I should've gone with Ethan. Or, you know what? I should've never accepted this slave life to these humans! I'd much rather be in the forest, trying to find a nice, female Pikachu, to settle down with. But, no, I ended up getting stuck here with you and your stolen gym badges.
Lyra: Woah, Pikachu!
Lyra: Since when can you talk!?