بسم الله الرحمن الرحيم
If any haram or impure substance like the blood or fat of pig or dead is mixed in the lipstick then it is haram and unlawful to apply it. We are not aware of the ingredients of Indian or Western lipsticks.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.