Yeah so that's the Gen IV Catch rate formula, where;

- HPmax is the number of hit points the Pokémon has at full health,

- HPcurrent is the number of hit points the Pokémon has at the moment,

- rate is the catch rate of the Pokémon (which may have been previously modified from the use of the Heavy Ball or Safari Zone modifiers),

- bonusball is the multiplier for the Poké Ball used, and

- bonus status is the multiplier for any status ailment the Pokémon has (2 for sleep and freeze, 1.5 for paralyze, poison and burn, and 1 otherwise).

- and A is the final catch rate

So lets do a little maths. For the sake of the question, lets assume you get Lugia down to 10 HP. I'm also going to assume that Lugia is 31 IVs, No evs- thats 164 HP Sooo;

a = [(3 x 164 - 2 x 10 ) x 3 x 1]/ (3 x 164)

= 2.878

So right now you catch rate is a measly 2.878

Which is more or less 3. o-o