The easiest and only way to get a lucky egg in Pokemon Fire Red is to catch a Chansey and hope it has one. The best place to do this is the Safari Zone.
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You can't.It's only obtainable in Fire Red/Leaf Green by catching wild Chansey in Safari zone.You can also get one by doing the Lucky Egg Quest in Pokemon XD:Gale of Darkness.It's far easier to get the egg in XD than in FR/LG.
The item Lucky Egg, that doubles the Exp.Points earned in battle, can be obtained by catching a Chansey in the Safari Zone. You will have to be lucky though, since there is not really that high percentage of getting a lucky egg with the Chansey you catch (and it is not easy to meet a chansey, nor catch it, either...). As a sidenote, I actually got lucky as hell and receive a lucky egg on the third Chansey I ever caught in Firered. If I forgot to mention it, the Chansey will be HOLDING the item, in case you are lucky enought to catch a chansey with it.
Don't cheat! Have a Pokemon that you want to train get traded to you have it hold a lucky egg and start battling trainers in no time your Pokemon will be level 100.
Training a Pokemon that was traded to you gives it boosted experience points when you win also if a Pokemon holds the item lucky egg you receive more exp points.
the togepi egg is in the water labyrinth on 5 island, not on 4 island