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The Event Hourglasses don't expire.
Here's a description comparison between the Event Hourglasses and Event Tickets (Meowth), which do expire.
The Meowth event tickets clearly state that they will be deleted when the event ends. The hourglasses do not, the event hourglass description even avoids any mention of the Lapras event specifically, instead alluding to 'Select Solo Battles or Events', which implies that it's for more than just the Lapras event.
