In Lakshya movie Karan Shergil (Hrithik Roshan) is a young man who has no actual goal in mind or plans for his future. He represents those urban youth in modern India, who have money but little ambition or purpose in their lives. His father is a businessman; his brother is a successful individual living in America, but Karan is drifting along. His girlfriend, Romi (Preity Zinta), a student activist and reporter who espouses fashionable causes out of well-meaning sincerity, tells him he needs to find a goal in life. When a friend announces he is going to join the Indian Military Academy, Karan applies as well, despite dissent from his parents.
Karan's first days at the IMA is a disaster. Because he is indiscipline and unused to a spartan existence, he keeps getting into trouble at the academy. Upset, he leaves the academy without permission, sneaking over the wall. Back home, his parents are unsurprised and even though they urge him to join the family business, they are disappointed with the way their son has turned out, especially in comparison to his elder brother. Romi, meanwhile, is tired of his aimless and indecisive ways and calls off their relationship. Karan finally comes to terms with his situation and makes his decision. He returns to the IMA, takes his punishment, and becomes a focused, disciplined cadet leader, graduating as an officer Lieutenant Karan Shergill.
Lt. Karan Shergill (the starting rank for all new commissioned officer in the Indian Army) is posted to the 3rd Battalion of the Punjab Regiment, commanded by Col. Sunil Damle (Amitabh Bachchan) somewhere in the Kargil sector, and handles his responsibilities well. From an immature teenager Karan transforms into a mature officer, he finally decides the essence of his life or his goal. Karan comes home on leave and finds out that Romi is getting engaged and goes to the ceremony to congratulate her. Back at home Karan is recalled to his post as his leave is cut short due to outbreak of hostlities in Kargil. He reports back to his post where he is promoted to the rank of Acting Captain . His battalion CO briefs the officers on the latest situation. The battalion has been assigned to secure Point 5179, crucial vantage point dominating the army's main supply line, the NH1D. The first part of the assault is successful and battalion destroys the enemy's screening units with Karan cited for his bravery in saving another officer's life. In the second phase of the assault Karan's unit engages in a failed attempt to storm and capture the Pakistani strongholds located on the mountain. The Pakistanis have the advantage due to their strategic position, and deal the unit heavy losses during the attack.
Capt. Karan Shergill and a group of 12 are next given orders to encircle the enemy position and attack it from behind. To do this, they must scale a 1000-ft wall of rock. After the unit sustains an attack in a grass field and loses their commanding officer, the remaining men scale the cliff and attack the Pakistani stronghold from behind during the night. The movie ends with Col. Damle looking out across the mountains the next morning, to see Capt. Karan hoisting the Indian flag atop the ruins of the stronghold. Later, it is revealed that Karan and Romi reunite.