First off: movesets.
Twisted Spoon is useless for Lugia because it has no offensive presence whatsoever, and it only boosts psychic moves. Dragon Claw is useless for Salamence since it only gives a 20% boost to Dragon type moves, which means all its other moves remain unboosted.
Fly = useless in competitive play. All moves that require more than 1 turn to be fully executed are worthless, because your opponent can fully predict when the move will take effect and either switch to a Pokemon with a resistance or use Protect/ Detect.
Why does Lugia have Rain Dance and nothing to benefit from it? Hydro Pump will get boosted in the rain, but no STAB and mediocre Sp. Atk; you're also missing EVs (I know this is Gale, but I'm going to use main line games as examples rather than a game that most people don't have the console for).
I had to say something about movesets, since I really don't understand what you mean by lead and support, or what you're trying to achieve with this pairing.
Lugia doesn't have any moves that will be of help to Salamence, it doesn't set up anything useful, nor does it have something like Heal Pulse which will benefit your attacker, nor an ability beneficial in doubles. Rain Dance actually makes the situation worse, what with Thunder being 100%. And why would you call your main attacking Pokemon 'support'?
Lead Pokemon: Pokemon that sets up the playing field with weather effects, hazards, or a status ailment. Also includes scouts who can use U-Turn/ Volt Switch, or Fake Out.
E.g., Politoed, sets up weather with its ability; Mienshao, Scarfed and scouts with U-Turn, or Life Orb Fake Out; Forretress, sets up hazards.
Support Pokemon: Pokemon that will heal the team or keep the team from being swept, such as walls for switch ins, or clerics to Wish pass.
E.g., Blissey, cleric; Bronzong, wall/ dual screens.
Those are the common meanings for Lead and Support Pokemon. Perhaps you should find different terms for what you're trying to say here, because I don't understand what role you've assigned to Lugia at all.
Pokemon that help attacking Pokemon in doubles are ones like Latias and Blissey, if only because of Heal Pulse. Latias can also set up dual screens.
I think a core picks up an all aspects on the other Pokemon.
Thing is, this pair doesn't. I think you should rethink another example to make yourself clearer?
But then you say before
I'm not implying a core team.
Then what are you implying?? Sorry, I can't figure out what you're trying to achieve with your pairing.
I'll put a doubles example below of a sweeper & a support Pokemon.
Scizor @ Life Orb
EVs: 252 Hp, 216 Sp. Def, 40 Atk
- Swords Dance
- Bug Bite
- Bullet Punch
Latias @ Light Clay
EVs: 252 HP, 252 Speed, 4 Sp. Atk
- Light Screen/ Dragon Pulse
- Heal Pulse
Chansey @ Eviolite
Ability: Natural Cure
EVs: 252 Def, 252 Sp. Def, 4 HP
- Heal Pulse
- Heal Bell
- Toxic/ Thunder Wave
The traditional "core" team in singles is something like Scizor and Rotom-W; this example sees Scizor take the Grass hits, and Rotom-W take the Fire hits. Cores consist of Pokemon that can wall each other's weaknesses.
Lugia and Salamence both have a x2 Rock weakness and a x2 / x4 Ice weakness (respectively). I know its harder to counter your partner's weaknesses in doubles, but having two Pokemon that can be swept by the same moves on the field isn't a good idea.