No. Air tickets for LTC must be booked through one of the three Authorized Travel Agencies — Balmer Lawrie (BLCL), Ashok Travels & Tours (ATT), or IRCTC Air. Direct booking from airline websites is not permitted.
Source: LTC FAQ 11
Can I book my LTC air ticket from the airline's website directly?
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This answer is for informational purposes only and does not constitute legal advice. Always refer to the original rules and consult competent authorities for official interpretation.