A trick to getting a Rare PURPLE beam in a Raid Den is to:
1.) Change text speed to Slow and save the changes. (Change text speed to Slow, click OK. Then, after that, SAVE game.)
2.) Put the wishing piece in the den.
3.) Before the text states that it's saving the game (and slowly reveals that the color of the den isn't Purple, but Red), click the Home Button.
4.) Close the game. (press X button to close game)
5.) Relaunch the game and repeat the steps until your Den shows a Purple Beam.
Here are the locations of Lapras Dens (They ALL have a chance that it'll have the HA):
Max Raid Battles: Bridge Field, Dusty Bowl, East Lake Axewell, Giant's Cap, Giant's Mirror, Lake of Outrage, South Lake Miloch, Stony Wilderness, West Lake Axewell
Gigantamax Raid Battles: Giant's Seat
Source: Experience and Patience