How can I cut back a very overgrown lawn for a robot mower

[MaggieBsBoat]

I’ve returned to my long-rented out house to a garden looking like this (picture taking a while) I’m a gardening newbie. What is the easiest way to cut back the lawn so that I can get a good robot mower to keep on top of it. Sorry for a stupid question. Also any tips on how to improve the lawn once it’s cut back would be highly appreciated! Thanks!

As the photo hasn't been approved yet we can only presume at the state of the lawn.

If it is very long, strim first and then repeatedly mow reducing the height of the blade each time.
If it isn't actually so long it needs a strim, just start to mow on a high setting and lower the blade go.

Strim, then mow cutting on a higher height for the first cut, 3 days later cut at your desired height if shorter. To improve the lawn buy appropriate mix from garden centre

How can I cut back a very overgrown lawn
The same way as you eat an elephant. One bite at a time.
Start on a high cut. Reduce the grass by a third every time you cut until you reach your required height.
Grass is tough stuff so you could cut low straightaway; it would recover but wouldn't look very nice in the interim. And it's not a very good strategy in the middle of a drought.

any tips on how to improve the lawn once it’s cut back would be highly appreciated
That's a whole book in itself! The easiest instruction is what you are going to do anyway: get your robot to mow regularly.
Grass likes fertile soil, wildflowers like poor soil. So get some goodness in the soil.

No pic visible, but I bought a house with very un cared for very long grass. I borrowed a big powerful mower, single blade type, highest setting & just blazed through that jungle with no grass collector on. Took a while, but it came back to a respectable lawn ok.

only addition is to aerate the soil. You can rent a hollow and tyne or buy a handheld machine it removes plugs of soil. The reseed / fertiliser.