If you have a NR LTC, I'd file 2+ months in advance. There is NO 90-day grace period for NR LTC holders (only for Residents).
If it is a Resident LTC, I'd file at least 3 months in advance, as some PDs sit on them for a few months, making the process take anywhere from 4 weeks to 6 months (depending on if the PD does their job timely).
"A man who trims himself to suit everybody will soon whittle himself away." - Chinese fortune cookie (but politicians should take note!)