A traditional historian, I am not, but I lecture on this subject in university classes and have taught broadly about this subject and specifically regarding the grass species evolved for mowing and grazing.
If you were to have looked out over your estate, it probably would have consisted of an inner and outer perimeter. The inner perimeter would have been guarded by gate or wall. It’s ground covering would have been exposed soil, mud, and maybe some native or naturalized plant materials. The most likely plant material would be grasses like Poa species and early successional dicotoledonous species, maybe clover. If you had a local source for stone or gravel, that would have likely been scattered for convenience of not walking in mud. Livestock would have grazed perimeter areas beyond your wall. You might have had tenant farmers or laborers manage cereal grains or fruit orchards beyond those walls. I am sure that the distance that “lawn” extended would vary greatly with land holdings, status, terrain, local flora (deciduous forest vs steppe vs jungle, immense variation even in northern Europe).
Modern lawns are areas maintained through mowing or grazing – the latter having had an effect on even modern day turfgrass species for many thousands of years. I previously mentioned the Poa species. These are some of the most wide spread species around the world – having the ability to move in animal feed, straws, mulches, ruminant animal stomachs, poop (AKA fertilizer to a 16th century serf). Today, some of the most common turfgrass species include those from Steppe regions of Asia and northern Europe that are 100s of thousands of years in the making due to the grazing experienced in that region. In northern Europe and the UK, you can experience a grazed landscape in traditional hay meadows. There are lots of examples worth checking out – just the pictures of them are emblematic of what would have been fairly regular in the 16th century grazinglands of Europe.
Lawns (at least the grassy stuff that we walk on in our modern lawns and gardens) are composed of grasses and amenity forbs (dicotoledonous, broadleaf plants like clovers or plantains, annual herbs, etc.). Modern lawns are an extension of our homes and incorporate many modern themes of cleanliness, tidiness, order, decor, etc.). Those aren’t new themes in the arc of human history. How we manage the landscape near our abodes is not just cultural, it likely stems from a subconscious early-human desire for safety, protection, food, etc. These principals would have had purpose in the 16th century just like they have for all of pre-modern history (my words, probably not the ones historians and anthropologists would choose). Those purposes would certainly include line of sight for defense (not getting taken by surprise, shooting arrows and throwing spears, controlling entry and exit, inviting trade, etc.), and communication (sentries setting fires, flagging, signaling, etc), but there are other easy to imagine reasons, such as ease of movement, reducing insect pests, increasing light for production of grain crops and grazing animals, and probably several others. The point is, for at least many thousands of years humans have felled trees, grazed, and gardened their immediate surroundings. This is partly out of necessity for food agriculture but also for defense - you can also relate to this if you’ve ever had to keep deer or rabbits from eating your garden plants. An aesthetic certainly would have developed to prefer stately grounds, but that would occur only in instances where safety and available time/labor existed first. Grazing would have prevented the succession back to forests, but by the 16th century, treeless landscapes would have been fairly common due to the need for lumber (not my field). The other major rationale for “lawn” that I’ve failed to mention thus far is sport or athletics. These sport grounds existed in pre-modern Americas. Check out Illinois Native American and Moundbuilding cultures in Americas. The idea of a lawn has changed – to the point that we are aware of ecological detriments associated with them. But the necessity and rationale for lawns has been around for a while. I’m on a small phone screen but would be glad if others would add to this. I’m also open to questions and dissent.