With the release of Litecoin Core 0.16.0, your machine's wallet can natively support SegWit transactions.
As always, it is important to back up your wallet, especially before making changes to wallet software.
Checking your version
You may check your current wallet version with:
If it's below 0.16, you may update the Litecoin Core wallet and thus enable SegWit.
Updating Litecoin Core
To update, run the script below:
curl -sS https://raw.githubusercontent.com/naconner/lamascripts/master/updates/nodes/ltc.sh | bash
If successful, it will output 'Litecoin Core is updated.'
Afterwards, check the Funding panel in your admin to verify the balance is seen and that the current deposit address begins with a 'M'. If so, your wallet has been successfully updated.
Please contact firstname.lastname@example.org with any questions.