You can have an environmentally friendly lawn just by NOT dousing it with chemicals and mowing whatever comes up. Plants other than lawn grass tend to have more environmental benefits.

Mow what grows, and create healthy soil with compost topdressing.

Lawn grass by its intrinsic nature is usually not environmentally friendly. It requires too much water and fertilizer, and does not provide an environment for butterflies and bees. The best you can do if you want to have a grass lawn is find the varieties of grass seeds that work best in your climate. There are some grasses that have been bred to need less water and fertilizer, so do an internet search.

To get better advice, you need a pic, zone and nearby city.

Agree with Sigrid. Plus, your idea of small is undoubtedly different from my idea of small.

Generally if you want to help the environment, stay away from fungicide, insecticide, and chemical fertilizers.

I would also add that planting a monoculture (a lawn, regardless if a blend of grass types) that does nothing to attract or provide habitat for pollinators or is not otherwise attractive to wildlife cannot be considered "environmentally friendly".

You want to encourage native grasses to grow, which will ultimately use the least amount of water, fertilizer and nitrogen. Check with your local university extension services to see if they have any guides online. You don’t want to just let it go without knowing what is growing there.

Once the OP returns with answers to Sigrid's questions, we can do a better job, as mentioned.

There are some non-lawn ground covers which attract pollinators. Dutch white clover comes immediately to mind. I believe red creeping thyme also does.

There are lots of other options that are not grass… are low growing.. need no mowing and little water… never mind much prettier than grass

Do nothing. Let whatever grows there, grow there. In my case, my lawn would quickly turn into poison ivy and thorny bushes. Eventually Bradford pears and tree of heaven would take over, but long before that, the county would likely condemn my lawn as a public nuisance.

Truth be told, covering your lawn with concrete may be the most environmentally friendly thing to do since it will require no maintenance and hence no electricity usage. Would help with local water levels too.

Concrete is ugly and definitely not environmentally friendly…come on …put your mind to it …you can come up with something better than that…weed cloth..pea gravel …and spaced succulents …?

Depends on how you define environmentally friendly. Are the Himalayas environmentally friendly? Most of them aren't much different than concrete.

A better idea would be to source recycled concrete chunks and use them to make a path through the lawn-replacement.

Well, if the only goal is to lower CO2 levels, then plant tall trees. Like I said, it all depends on how you define helping the environment.