In Ramayana, Indrajit was able to hit Laxman by his special weapon named Shakti. Due to this Laxman went very near to death. Now Lord Hanuman went to Himalaya & brought Sanjivani. This way Laxman was saved.
The next day Indrajit uses all three main weapons i.e. Bramhastra, Narayanan's Sudarshan Chakra & Shiva's Pashupatra (Trishul). These weapons are considered as most deadly weapons but none of this weapon was able to harm Laxman.
First of all, Indrajit never tried to use a Brahmastra, Narayanastra or Pashupatastra in the war (although he did use a Brahmastra against Hanuman during Hanuman's pror visit to Lanka, as I discuss in this answer). But he did once use another weapon of Shiva, the Raudrastra, although as I'll discuss below that was just to fight off one of Lakshmana's weapons. Second of all, the TV serial is conflating a bunch of different incidents:
There is one occasion where Indrajit fatally wounded Lakshmana, but that's an occasion where he fatally wounded both Rama and Lakshmana. As described in this chapter and this chapter of the Yuddha Kanda of the Ramayana, early on in the war, Sugriva's nephew Angada defeated Indrajit in battle, so Indrajit turned invisible and then launched numerous Nagastras (snake weapons) at Rama and Lakshmana, which put them in a state very close to death. But then Vishnu's mount Garuda came to the battlefield, eating all the snakes and healing the wounds of Rama and Lakshmana. (Rama asked him who he was and why he was helping them, but Garuda refused to answer because Rama wasn't supposed to know that he was an incarnation of Vishnu.)
The only direct confrontation between Lakshmana and Indrajit happened later on in the war, and its conclusion is described in this chapter of the Yuddha Kanda. Indrajit fired a Yamastra (weapon of Yama god of death), but Lakshmana destroyed it with a Kuberastra (weapon of Kubera god of wealth). Then Lakshmana launched a Varunastra (weapon of Varuna the ocean god), but Indrajit destroyed it with a Raudrastra (weapon of Shiva). Then Indrajit fired an Agneyastra (weapon of Agni the fire god), but Lakshmana destroyed it with a Saurenastra (weapon of Surya the sun god). Then Indrajit launched an Asurastra (weapon of the demons), but Lakshmana destroyed it with a Maheshwarastra (another weapon of Shiva). Finally Lakshmana hit Indrajit with an Indrastra (weapon of Indra king of the gods), killing him. Now after killing Indrajit, Laskhmana did have some wounds, but those wounds were very easily healed by Sugriva's father-in-law Sushena.
The incident you mentioned involving Hanuman carrying a mountain happened even later in the war and had nothing to do with Indrajit. As described in this chapter of the Yuddha Kanda, during the battle between Rama and Ravana, Ravana's brother Vibhishana killed Ravana's horses, so Ravana got down from his chariot and threw a powerful spear at Vibhishana, but Lakshmana shot the spear down with three arrows. Angered by this, Ravana threw an even more formidable spear at Lakshmana, fatally wounding him. So as described in the next chapter, Sugriva's father-in-law Sushena sent Hanuman to retrieve the herbs called Vishalya Karani, Savarni Karani, Sanjiva Karani, and Sandhana Karani from the peak of Mount Oushadi. Hanuman couldn't identify the herbs on that mountain, so he brought the mountain peak itself to Lanka, and then Sushena used the herbs to heal Lakshmana.
So there's not even a question of Lakshmana being vulnerable to some Astras (magical weapons) and not others, because there iss never an occasion where he shows any invincibility against Astras.
The fact is that both in the Ramayan and Mahabharat the so called good sides(i.e. Sri Ram's side and the Pandavas respectively) were weaker than the bad side (Ravan's and the Kauravas respectively). So the good side cheated to win, plain and simple. Ram and Laxman even though they were avatars could not have defeated indrajeet had not vibhishan betrayed indrajeet. Ram and Laxman broke the rules of war and attacked indrajeet while he was praying. Regarding angad defeating indrajeet, so that did not happen, angad killed his charioteer and killed his horses but he was not able to defeat indrajeet once he started using maya tactics infact Indrajeet was actually stronger than GOD......
Like any library, Hinduism Stack Exchange shares great information, but does not offer personalized advice, and does not take the place of seeking such advice from any Acharya, Pundit, astrologer, Guru or other trustworthy Counselor.