If you are on Linux Ubuntu 16.04, follow those steps (cut and paste one line at a time in a new Terminal window):
**** ensure that the system is up to date ****
sudo apt-get update
sudo apt-get upgrade
sudo apt-get dist-upgrade
sudo apt-get autoremove
sudo reboot
**** download the source code ****
mkdir Github && cd Github
sudo apt-get install git
git clone GitHub - litecoin-project/litecoin: Litecoin source tree
cd litecoin
**** Install the dependencies ****
sudo apt-get install build-essential libtool autotools-dev automake pkg-config libssl-dev libevent-dev
sudo apt-get install bsdmainutils libboost-system-dev libboost-filesystem-dev libboost-chrono-dev
sudo apt-get install libboost-program-options-dev libboost-test-dev libboost-thread-dev
sudo apt-get install libqt5gui5 libqt5core5a libqt5dbus5 qttools5-dev qttools5-dev-tools libprotobuf-dev
sudo apt-get install libqrencode-dev protobuf-compiler miniupnpc
**** To install the deprecated version of Berkeley DB 4.8 ****
sudo add-apt-repository ppa:bitcoin/bitcoin
sudo apt-get update
sudo apt-get install libdb4.8-dev libdb4.8+±dev
**** Compile ****
./autogen.sh
./configure
make
**** Optional *****
sudo make install
**** Execute ****
cd ~/Github/litecoin/src/qt
./litecoin-qt