Lakshmana

 

If Lord Lakshman would have died due to the javelin shot by Indrajeet would Lord Ram have given up his life or would he have continued to battle? And if he continued to battle who would have won Lord Ram or Ravana?

Firstly, it was due to Ravana's Brahma spear that Lakshman had fallen unconscious, not due to a javelin shot by Indrajit.

Now, when he got hurt due to the spear, Lord Lakshman remembered subconsciously, who he was i.e the form of Vishnu and the direct avatar of Ananta Shesha. And using his divinity, he remained alive. So, anyway it wasn't possible for him to die due to that spear.

Just in case, he had died, two things would have happened. Either Lord Ram would have burnt the entire army of Ravana in rage with some arrows. He had clarified many times that he and Lakshman were one soul, and they could never be separated. Or, he would have given up his life with his brother unable to live.

But as the second event cannot happen, Lord Ram would have destroyed the Rakshasa army in rage and probably even destroy the creation due to his energy.

It was good luck for Ravana that Lakshman didn't die.