^^ My mom is pretty close to the wife half of the couple who mowed the lawn.
So I'm guessing they knew your mum was very ill, and were close enough to know - not just assume - that mowing the lawn would be seen as a "This is wonderful, our neighbours care about us and have done this to help out" thing rather than a "wow, maybe they're upset our shaggy lawn is bringing down the look of the place, now I feel bad" thing. I'm also guessing that they really do
care about your parents and meant it as a kind gesture. All is well! (And your parents have awesome neighbours.
I hope your mum's health is improving.)
I've had neighbours that were that nice, where we were on the right sort of terms for us to be comfortable helping each other out with things like that. I've had neighbours that were nice, but kinda prickly about their property and territory, and while we were on the right sort of terms to offer
to help each other out, doing it without asking would have completely crashed the relationship
. I've also had neighbours that were completely standoffish, never tried to get to know us, didn't want to, and whose idea of polite interaction was to get the body corporate manager to write me a letter threatening to report me to the local authorities for having an illegal fountain setup during a drought (I didn't
); if I'd decided to "do a nice thing" and gone on their property to decorate it without their knowledge or consent right after they moved in and before I knew what they were like, there would have been war
. Honestly, Alicia's neighbours are really lucky that she's the sort of person she is - this could have really easily been a "My friend feels the neighbours violated her boundaries and now there's a feud starting" sort of post!