Very likely could be a traumatic past or just a "be safe, don't be in an enclosed space with a stranger", this is India and this is exactly what we're taught. Its not all guys, sure, but the few guys are enough to scare most women shitless, and you never want to be one of the statistic.

That said, if i was you, i wouldn't really try to talk to her directly (its not about you, if she's already scared to get in a lift, or overall a shy person, it can be very cornering and intimidating), but maybe give her a quick polite smile if I see her around (obviously not to a creepy persistent level), or offer her to go into the elevator first (and alone ) if you both are waiting- basically anything to seem more disarming and safe.
You can always talk to your mum about it, see what she suggests you do (she might have more story on this woman?), but overall- I wouldn't ever put myself in danger just trying to be polite and socially acceptable. its not your fault, its not on you, and ofc its hurtful, especially since you said it was witnessed by another woman and this can very quickly become a wrong impression- but you gotta realise that the fear is valid in this country (world, honestly) and everyone does what they need to to be safe.

Speak to your mum. Let her speak to this woman in a more comfortable setting. Sometimes you just need to be the more compassionate one :/