A retort in two parts.
"Capitalist acts..." - we'll leave that one 'til i pretend to give a shit.
Lawns? That most hated, useless, fucking obscene artifact of american imperialism; the pre-eminent badge of the petit-bourgeusis (sp??), and you choose that as the foundation upon which to bear your arguments?
Unless you have a couple of dairy sheep in your front yard, the 'lawn' serves no biological purpose - indeed the entire fucking purpose of the lawn is to declare that you can waste the resources that grassland should be providing.
Now, that said, there is only one way an anarchist society would require a lawn care service - if me, and mine, everyone of our kith - were dead and buried and rotted away.
"The customers will pay me, and I will pay you. Every party to these transactions is satisfied with them."
Wow. Whole lotta presumptions goin' on around there.
a) Anarchist society.
ergo - everyone's food, shelter, clothing, and other material needs are provided by some aspect of the gift economy.
Therefore, _No_One_, (!!!) could be _compelled_ to do anything they didn't want to do, for money (which is now totally useless, even as asswipes) or for otherwise. If you want to found the Manchester Free Lawn Mowing Society, then have at it... ; but i fear your client list and you labor list will both be thin as poor house gruel.
b) ergo - money is useless. (if i have to explain this, i may as well learn took.)
c) non-sequitor -- if you get your ass kicked (in your imaginary future society), it'll not be because of any ideological disagreement; just that your neighbors can see you for the asshole you are.
[* If admin thinks that crosses some line, they are welcome to delete it. For myself, i'll wear it.]