I'm glad a few other people have agreed with me about not 'owing' your parents anything. The clue is in the word 'owe'. I think it's lovely if you have things in common with your parents and like spending time with them, but to 'owe' them or to repay a debt for their input and sacrifice is just not a healthy relationship in my eyes.
It's a bit like siblings - some people are really close with their siblings, they become friends, they keep in touch all the time and become like friends. Other siblings have naught in common but birth and see eachother only because of family events. Sometimes that happens with parents - the only thing that ties you is blood and as you get older, you drift apart.
Also I think that some parents totally define themselves by their role of parent and then when their child becomes independent and isn't this 'disney matriachal' family of everyone popping in every day, the mother figure feels worthless and as though her life's work as a mother has been in vain. Because she hasn't rounded out her life to define herself with work or hobbies or friends.
Living through your children, or for your children, can leave you sorely disappointed if they don't match up to the expectation you drew for yourself.
I also think it's often worse in divorced families - mothers sacrifice even more of themselves and become quite emotionally enmeshed with their kids, whereas dads have more money and freedom to self-actualise and live whole lives and 'need' their children's validation less. This lack of 'neediness' actually draws the kids closer. Funny how that works out.
I also think that fundamentally, in the case of my parents and mother in particularly, she has no idea what sort of life I'm juggling. She was looking after us but had no money worries, a lovely home, a husband bringing in lots of money, didn't have to work. Meanwhile, I have a career where I'm in charge of large budgets, a large team, and strategic oversight of my entire department as well as juggling childcare, being an attentive parent, giving my parents attention, trying to keep a relationship on track and juggling multiple parts of a blended family. She had nothing to do with her parents or in laws at my age. It's chalk and cheese what we're comparing too. She says we are/were 'equally busy' but I don't believe it and I get cross when she can't take the initiative to organise a lunch for us given she works 2 days a week and has so much less on her plate. And then I get the blame for not being proactive enough because I just have no brain space left to also plan yet another thing.
So I would say, put the effort in, book the restaurant, tell them the date - they may just turn up. But if you expect them to do the organising, it will likely not happen.