Even with Israel being a tiny little bit paranoid about security I'd also second your choice and do nothing. While LX doesn't pay out EU compensation according to their "upgraded" ruling regarding delayed flights, they do when it's about a cancelled flight.

I'd not keep your hopes up too high for it to happen (and it's still a fight..) but I doubt there is any risk with arriving alone in TLV when your original booking had two pax on them. I'd probably feel even "safer" to do this at any other airport, but especially for a not-too-young mother, I doubt they'd find it suspicious. They might very well ask about it, though at the interview, and it might possibly lead to a higher number category (usually 2+ pax travelling together get lower numbers in average than single travellers)