If you have successfully entered your Transaction PIN and Email Confirmation Code to confirm the Litecoin (LTC) withdrawal from your account, then it will be sent within 10 minutes unless for some reason the hot wallet balance is low and needs to be topped up. Cryptocurrency withdrawals that are not completed within 15 minutes will display a "cancel" button in the Pending Withdrawals section which you may click to cancel, returning coins/tokens back to your balance.
If your transaction has been sent you will see its status marked as "Complete" within your account Withdrawal History and next to it an icon that links to a block explorer which verifies your transaction has indeed been sent and has confirmed or is confirming on its respective blockchain.
Once its confirmations have reached the number your wallet provider mandates, you'll then be able to spend/move/trade those coins/tokens — for specifics, please contact your wallet provider.
If the number of confirmations has reached the number your wallet provider mandates but doesn't appear in the destination wallet, you will need to contact your wallet provider's customer support and provide them with the Transaction ID so they can trace it.
Important: As noted on the withdrawal page, "Withdrawing to a different currency's wallet address may result in the loss of your coins/tokens. Please only withdraw to a wallet address dedicated to Litecoin — known ticker symbol for Litecoin is LTC." Once you authorize a withdrawal and it is sent, QuadrigaCX no longer has any control over your coins/tokens.