ЛЁГ (лог-, лож-, лаг-, леж-, леч-, ляг-, ляж-, лёг-) 'lay, lie, put; -pose, -pone'
предлћг preposition предлћжный prepositional положќть put, lay
предлагђть propose предложќть propose лежђть lie
ложќться lie down предложљние proposal отложќть postpone, put off
лљчь, лїгут, лїжет; лёг, леглђ lie down
There is a different root that looks like this one in some of its forms: ЛЁГ as in лёгкий 'easy'. It is a different root because it has a different meaning as well as different variants.