Keep on and Live on

Keep on verb - Allow to remain in a place or position or maintain a property or feature.

Live on and keep on are semantically related in continue topic. In some cases you can use "Live on" instead a verb "Keep on", when it comes to topics like persist.

Live on verb - Continue to live through hardship or adversity.

Keep on and live on are semantically related in continue topic. You can use "Keep on" instead a verb "Live on", if it concerns topics such as persist.