In my opinion, if your lawn has been seeded for 100 years it is likely that it is "Perennial rye-grass" (Lolium perenne L., fam Graminaceae), traditionally used for lawns.
Your lawn has not been treated for some time, so of course it may grow many kinds of grass, some naturally led by the wind, and more.
To keep a good lawn in shape you should do the following:
- Clean the weeds
- Aerate the soil
- Periodically re-seed
- Water properly (few, deep waterings are better than many light waterings)
- Mow weekly
To repair worn areas, you have two choices:
The first, quick but quite challenging, is plowing or digging in the damaged areas and proceed as if it were a new lawn. There are commercially meadows ready, sold per square meter, that can be easily placed, after treatment of the soil.
The second, simpler but much longer, is a simple clean from weeds, good aeration and fertilization and re-seeding.
In a field so worn out, it's definitely happened that the causes indicated in other responses (trampling, insufficient watering) were added to a low shearing of the lawn. In this way some plants, the strongest, have survived and grew at the expense of the weaker. Their root system has occupied vast areas of land, preventing the weaker grow. This explains the empty areas.
First of all it is necessary to aerate the soil. Then you can proceed with a pitchfork, but being the ground is rather large I would recommend at least one pass with a harrow cut, which cuts the root system of the turf and allows you to move the ground to reseed. Multiple passes with a harrow cut are even better. Weeding with the whole root also helps to moves the earth.
Maybe you can rent a harrow of this kind above. Next, you will a tool like this below, to pierce the ground and keep it ventilated. Used periodically, this improves both the aeration and the drainage.
Once your lawn has been treated with a good lawn fertilizer you can proceed to re-seeding or simply wait for the old grass rhizomes, left in the soil, to germinate into new plants.
In the meantime, you have to water a lot, even throughout the night and during the hottest hours. And proceed to shear weekly, that prevent the plants from growing too much, taking away space and nutrients from other weaker plants.
Keeping the grass short and wet is the best way to grow a great lawn.