Can the HAL Lca Tejas perform Pugachev's Cobra maneuver?
No.
With that delta wing shape it will have pitch control problems at higher angles of attack. The Cobra maneuver requires a small pitch-down moment over the post-stall region up to 110° angle of attack. I very much doubt that this wing planform will have such pitch characteristics, and without thrust vector control a docile pitch behavior is a prerequisite for the Cobra maneuver.
In the development of the LCA a high lift coefficient without leading edge devices was the main goal of the wing design. It should be able to operate in the vicinity of flocks of birds - birdstrike is a real risk on many Indian Air Force bases. At the same time, the small aircraft should be able to fly supersonically, which lead to the double-delta wing as the best way to achieve both goals, and poor post-stall pitch response had to be accepted.
When HAL switched from MBB to Dassault for technical support, leading edge devices were added in order to fulfil the take-off and landing requirements. Post-stall flight was not seriously considered at any point in the development.