2 months over due! Would you take a money off tesco voucher in 2 months late and expect it to be honoured? No! Just because it was verbal/ face booked doesn't mean it can be any time.
I don't do lashes, but what's the time frame expected? What's the aftercare?
Is she following after care? If not they won't last, if they are meant to last a week, then a week ad a day later its a tough titties scenario.
She's clearly a something for nothing person, who when paying the going rate expects miracles.
Personally, I would reply with
"Hi x, I'm sorry you have been experiencing personal problems. As per our messages/conversation on *date* the offer was for January, as its now *todays date* I can no longer honour the offer.
I now use *brand* lashes, if you would like to try these, a full set are £x. Name x"
Expecting last months offer is reduculous anyway, and I'm quite shocked you have given in then, but that's the past, in future don't deviate from advertised offers/prices, and if someone books a service for past its cut off date while its running just remind them during booking that it will have ended then or they can book before date to get it for £x (makes you sound like you want to save them money and care about their pocket, but still says "the offer has ended and you know it has so don't bother trying it on") xoxo