WHIRLWIND EXPLANATION: Pokémon have a fixed, permanent score from 0 to 31 for each stat that affects how good that stat can ever get.

This calculator will figure out that score (called a "gene" or, more obtusely, an "IV") for you, so you can discard the unworthy. It's more accurate for higher-level Pokémon, so it's helpful to go into a level 100 wifi battle with someone and check your Pokémon's stats from there.

Stat calculator

Lugia
Lugia 		Base
stats		 Stats Effort Stats Effort Possible genes (IVs)
Level Level
HP 106
150–164
28–30
Attack
−10%
 90
77–89
16–17
Defense 130
122–135
23–24
Special Attack 90
86–99
31
Special Defense
+10%
 154
157–172
28–29
Speed 110
104–117
29–31

Hmm, I need more information to figure out your Pokémon's genes exactly. Try raising it to level 46 and entering its new stats.
Remember: if your Pokémon battles at all, you'll need to track the effort it gains. Consider saving your game and using Rare Candy instead.

And for your copy/pasting pleasure:

28–30 HP; 16–17/23–24 Physical; 31/28–29 Special; 29–31 Speed

or start over