First of all, even if the people in positions like this were only working for sustenance and UBI provides it for them, it doesn't mean some wouldn't want to continue working to make even MORE money. UBI is a baseline, not welfare. If previously a lawn mowing job was only enough for rent and food, maybe now with UBI it'd be enough for rent, food, and the occasional dinner and a movie. Ain't nothing wrong with that.
But you're right, at least some people would definitely completely exit the work force. Well, that just means the salaries of the rest would go up. Simple economics. Does that mean that some working families can no longer afford to pay a new immigrant bottom dollar to mow their lawn and instead have to pitch in themselves? Maybe so. Is that so bad.
Okay, you say, but what about those working mothers that are barely making enough money to be able to afford the most basic child care while they make their income? Good news - UBI also helps THEM too so either they no longer need to work if all they're doing is getting by to keep a roof over the child's head, or they have enough extra to pay for the increase in child care.
I'm not saying "don't worry about, it'll all sort itself out". This is a very complex policy with millions of consequences to our societies - intended and unintended. A lot of research must be done, and also experimentation. But to say that with UBI everyone would be worse off is ridiculous bordering on propagandistic.