At the end of season 2 episode 1 , Saitama asks King if he's going to keep lying about being strong and King says he doesnt know. Then Saitama tells him he could quit or get stronger. Did King get any stronger as the story continues? (in the manga)
He supposedly develops a guilt and fear due to the lie he is hiding from others. According to the wiki,
...he decided to visit Bang in his dojo and asked him to train him, in order to become stronger. After getting rejected however, he desperately tried the same with Bomb's dojo and later visited one dojo after another, only to get rejected over and over again, thus making him even more desperate. As a result he eventually dropped the thought of getting stronger and even considered the idea to die while attempting to fight a monster.
Unless he has the drive or the will to become stronger again in the future, then no, he will not get any stronger anytime soon.