There is not a red Gyarados in Lake Verity. The in-game report of a sighting is simply a story mechanic to get the player there. This little story element is a reference to the Red Gyarados in the Lake of Rage on Pokemon Gold and Silver.
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You have to go to the Lake of Rage. In the middle of the lake, there is a red gyarados. This is your only chance to catch the Red gyarados, so save before battling it to have multiple chances to catch it.
in johto, go to lake of rage and in the lake is a gyarados [it's red] defeat or capture it and ya'll receive the red scale.
Previous: {A red Gyarados is a shiny gyarados, and to get it you probably have to fish alot. Your chance of finding it is like 1 out of million. You can get it easily in GSC though. or trade the blue garados with the red scale from gold and put it into yours. it retains its shiny status} Alternate way: Make sure that you have caught all three beings of emotion: Mespirit, Azelf, and Uxie. Go to lake verity and fish around with a super rod. In about 20 mins, you should have one. I tried this a little while ago and it actually worked. I am now enjoying a red gyarados.
After you catch the Red Gyarados, Lance will be at the shoreline of The Lake of Rage.
The Red Gyarados is unique among shiny Pokemon as it actually first appears as a part of an event. Players first encounter the Gyarados at Lake Rage and have a chance to catch it before engaging Team Rocket.