Benefits of a small Garden or lawn in a small house.
Imitation of 'Nature' in the form of Garden / Lawn was a healthy habit of the past trying to remain close to nature and get reminded of their benefits - Green surrounding has always been pretty encouraging / motivating; the cool breeze through the garden has a different impact than modern AC; Natural colour of true unimitable colours of the varied flowers have altogether a different impact on the mood of humans. There are other lessons that one can learn - harmony among varied plants and deriving the resources to the extent that each one requires without conflict with others. There are innumerable benefits if one sits on it seriously, please.
A place to relax, rejuvenate and enjoy with yourself, family and friends. I remember my childhood, my parents, and my brother and me used to have our evening tea in our small lawn. It used to be amazing experience, So yes it is important and beautifies your home and surroundings.
In Spain we have "huertum", (http://huertum.com/huertum-en-el-primer-proyecto-europeo-de-agricultura-social/)the firsten European project of social and environmentally-friendly agriculture. Their goal is to spreed the word of how to make your own vegetaable garden at home/flat/city.
FASST (Formazione per Agricoltura Sociale e Sviluppo Territoriale) is the name of the project.
This cain of project should be in every city. I recomend them!.