Yes. You'll need to backup the wallet.dat file from litecoin core on your PC, transfer it to your laptop, then replace the wallet.dat file in your laptop with the one you grabbed from your PC.
How to Backup Litecoin Core
- Open Litecoin-QT
- File-> Backup Wallet
- Save it
- Grab a USB
- Drop the newly saved wallet.dat file into the USB
How to Insert wallet.dat into New Litecoin Core
- Download Litecoin Core but do not open it.
- Open your file explorer and type the following line:
- Delete the wallet.dat file in the Litecoin folder. Rename your wallet.dat file from your PC to "wallet.dat" if you need to. Drop it in the Litecoin folder.
- Open Core and if you see unconfirmed tx it worked.
You can dump priv keys to the addresses that received LTC and sweep it into Electrum-LTC. Only download this from Electrum-LTC.org. Electrum-LTC is a light-weight client that references other Full Nodes so you don't have to use your own. This means you don't have to keep your laptop on to stay up to date with the most recent blocks in order to send LTC. But if you want to keep supporting the LTC network by running Litecoin Core, then kudos to you!
How to Dump Priv Keys from Litecoin Core
- Go to console in Litecoin-QT
- type: walletpassphrase "your walletpassphrase here" 600
- type: dumpprivkey [your Litecoin address here]
Sweep into Electrum-LTC
- Open Electrum-ltc. Go to Wallet-> Private Keys-> Sweep.
- Input the private key and an LTC address you want to send it to. Often times, Electrum-LTC provides one for you.