Is it a crime to lie under oath in India?

Yes.

Any person can initiate Perjury Proceedings

Section 340 of Cr.P.C. contains the law procedure that has to be followed in Perjury proceedings.

Section 195 of Cr.P.C contains offences against public justice and for offences relating to documents given in evidence.

Court can initiate Perjury Proceedings, Suo moto

Section 344 of Cr.P.C contains the law procedure that the Court can invoke against any witness appearing in such proceeding who had knowingly or wilfully given false evidence or had fabricated false evidence with the intention that such evidence should be used in such proceeding.

These are 24 various provisions under the Indian Penal Code (IPC) that cater to definition and punishment for various perjuries of opposite parties and other public servants.

IPC 191: Giving false evidence
IPC 192: Fabricating false evidence
IPC 193: Punishment for offenses u/s 191 & 192 IPC
IPC 194: Giving or fabricating false evidence with intent to procure conviction of capital offence
IPC 195: Giving or fabricating false evidence with intent to procure conviction of offence punishable with imprisonment for life or imprisonment
IPC 195A: Threatening any person to give false evidence
IPC 196: Using evidence known to be false
IPC 197: Issuing or signing false certificate
IPC 198: Using as true a certificate known to be false
IPC 199: False statement made in declaration which is by law receiva­ble as evidence
IPC 200: Using as true such declaration knowing it to be false
IPC 201: Causing disappearance of evidence of offence, or giving false information to screen offender
IPC 202: Intentional omission to give information of offence by person bound to inform
IPC 203: Giving false information respecting an offence committed
IPC 204: Destruction of document or electronic record to prevent its production as evidence
IPC 205: False personation for purpose of act or proceeding in suit or prosecution
IPC 206: Fraudulent removal or concealment of property to prevent its seizure as forfeited or in execution
IPC 207: Fraudulent claim to property to prevent its seizure as forfeited or in execution
IPC 208: Fraudulently suffering decree for sum not due
IPC 209: Dishonestly making false claim in Court
IPC 210: Fraudulently obtaining decree for sum not due
IPC 211: False charge of offence made with intent to injure
IPC 219: Public servant in judicial proceeding corruptly making report, etc., contrary to law.
IPC 228: Intentional insult or interruption to public servant sitting in judicial proceeding

Terms used in judgments are misrepresentation, unclean hands, fraud on court, misuse administration of justice etc if you are searching for judgments online.

Here are the judgments for your usage in your cases under above IPC sections.