**Soulsliver Only.

It's alright...but I'm against using sleep during encounters like this but don't mind using paralysis as an alternative to avoid fainting it with burn, poison or confuse though...good work...

In HeartGold, Lugia is at lv70, isn't it?
At lv70, Lugia knows Aeroblast, Punishment, AncientPower and Safeguard. You might want to bring in a Steel-type with good Special Defence, as it will resist all of Lugia's offensive moves. Alternatively, use any Pokemon with very high Special Defence, a sleep-inducing or paralysing move and possibly a healing move.
Be wary of Safeguard! It makes it more difficult to use sleeping moves to capture Lugia.
(Also, despite Lugia's preferred habitat at the bottom of the sea, Dive Balls will be as useless as regular Poke Balls.)

....And what about Ho-oh?
Well, to take it down in HeartGold, the best course of action would be this:
1. Bring along a Pokemon with good Attack and Special Defence, with a sleeping move and False Swipe
2. Put Ho-oh to sleep and bring its HP down to 1
3. Switch to a Blissey with Sing/Thunder Wave and Softboiled, or similar (you need a special sponge for this one!)
4. Subject Ho-oh to a barrage of Ultra or Dusk Balls
5. If you're using sleep to make it easier to catch, you'll need to put it back to sleep when it wakes up. If you're using paralysis, you may need to soft-reset if Ho-oh runs out of PP
6. Keep going until Ho-oh finally succumbs. Gotcha!

At lv70 in SoulSilver, Ho-oh also knows Safeguard, Punishment, AncientPower and its signature move (Sacred Fire). Unlike Lugia, however, Ho-oh at lv70 can counter Steel types with its signature move.
Again, you'll need a Pokemon with high Special Defence and a sleeping or paralysis move, and preferably a healing move as well.


...At least, that's the technique I'll be using.

I used an spiky-eared Pichu with a Focus Sash to paralyze it, and then spammed False Swipe with my Gallade until it was down to 1 HP, switched to a Palkia I brought over from Diamond, and then threw endless Ultra Balls. The first time, it ran out of PP and fainted from using struggle

BTW, does the Focus Sash only have two charges or something? I couldn't find it after another battle where it was used.

Good Stradegy & no the Focus Sash shouldn't dissappear after any amount of uses or even when the opponent uses Knock Off...it's just that it only works once in a single battle then it's a done deal til afterwards...