In Pokémon FireRed & LeafGreen Versions, is there a known optimal or near optimal team with which to defeat the Indigo Pokémon League 200 times?
While Mewtwo would be helpful, at the same time you probably should have a party of other strong Pokemon with varied coverage to, more than anyhing, 1HKO the League's Pokemon. Without knowing what Pokemon you have or what TMs you have available all I can do is go over the League's Rematch teams you'll be facing each time:
Lorelei: Her rematch team is Dewgong, Cloyster, Piloswine, Jynx, and Lapras.
- An Electric-type would be real helpful dealing with Dewgong, Cloyster, & Lapras. (If you decide to use Zapdos be careful as it's weak to Ice)
- A Fighting-type could work too against Dewgong, Piloswine, & Lapras. (Note Lapras knows Psychic)
- Finally a Fire-type can also deal with the Piloswine & Jynx. (Piloswine has Earthquake)
- If you end up having them, Water-type deals with Piloswine and Ghost-type deals with Jynx.
Bruno: Steelix 1, Steelix 2, Hitmonchan, Hitmonlee, Hitmonchan
- Special Fire-types can handle the Steelix, notably Moltres & Charizard will be immune to their Earthquakes (watch out for Rock Throw on the one he sends out first).
- Fighting-type can also be good against Steelix but just be aware it has a LOT of Defense.
- Psychic-type eats Hitmonlee, Hitmonchan, and Machamp (you could maybe use a Flying-type but all of them have a Rock-type Move).
- If you end up having them, Water-type would probably be the best choice against Steelix.
Agatha: Gengar 1, Gengar 2, Crobat, Misdreavus, Arbok
- A fast Psychic-type (aka Mewtwo) would be prime here as it can most likely take out the Gengars & Crobat (and Arbok) before they can act.
- An Electric-type is also good for Crobat.
- Misdreavus should go easily down to a strong enough Physical attack, or a couple of strong Special attacks.
- Ice-type can be handy for Crobat but you have plenty of options for it already.
- If you end up having them, Ghost-type obviously would deal with the Gengars and Misdreavus (they I'd suggest a Ghost Move instead of a Ghost Pokemon; aka Mewtwo with Shadow Ball).
Lance: Gyarados, Kingdra, Aerodactyl, Two Dragonites
- Electric-type easily handles Gyarados and deal with Aerodactyl (just be careful as Aerodactyl is fast and both of them have Earthquake).
- Kingdra is tricky as it's only weak to Dragon and decent equal defensive stats. It knows Hyper Beam, Dragon Dance, Surf, and Ice Beam, so best I can suggest is a bulky Pokemon not weak to any of those Moves. (Reminder, move Category goes off Type this Gen, so after a Dragon Dance that Hyper Beam is going to hit harder in addition to it just being faster).
- If there's any reason to have an Ice-type on your team it would be for the Dragonites. (If you use Articuno watch out as the Lv66 knows Flamethrower and the Lv72 knows Thunderbolt; Infact instead if an Ice Pokemon you may want to consider a bulky Water that knows Blizzard or Ice Beam).
- If you end up having them, Water-type can also be used against Aerodactyl (and learn Ice-type Moves as I said). And if you can get a Dragon-type Move or have the patience to train up a Dragonite or can get your hands on a Kingdra, they wouldn't be bad to have either if not just the raw power but to deal with Lance's Dragon-types.
Blue: Heracross, Alakazam, Tyranitar, (Exeguttor/Venusaur), (Arcanine/Charizard), (Gyarados/Blastoise)
- Fire-type should be good enough for Heracross, Exeggutor/Venusaur (note Venusaur knows Earthquake). If you end up having a Flying-type it'll also be good against them too (Heracross has Rock Throw).
- A strong Physical Move can take down Alakazam, but if you have a Ghost-type move even better (this also goes for Exeggutor).
- Tyranitar is a tank that is quad weak to Fighting-type but it knows Aerial Ace. If you have a Water-type will be good here but it also knows Thunderbolt.
- Speaking of Water-types, you know what you may as well have one as it'll be good against Arcanine. As well as Ground or Rock, but I'm trying to keep this as streamlined as possible.
- Finally Electric-type for Gyarados, Blastoise & Charizard.
- The Psychic-type and Ice-type would also handle Venusaur.
So, yeah, so at you can see the most helpful Types (at least in my opinion) would be Electric, Fighting, Fire, Psychic, and Water; meanwhile would be very helpful to have a Ghost and Ice move.