A bit of a strange one. The smaller stones that could be part of a circle are mainly buried in clumps of heather, but they could form a circle....I guess.
J.Barnatt has the circle down to a fortuitous arrangement of stones.
Sadly the rocking stone marked on the late 1800's O.S maps is no longer rocking. A familiar tale in Derbyshire.
I had a feeling for sometime that the stone features mentioned by Flopsypete to the south of the circle were associated with a medieval farm/settlement.
Remembering to check them out last time I was up there.....I'm pretty certain that they relate this settlement. The structures, marked in places by upright stones, are in fact the remains of a long house, a smaller building and an enclosure wall.
Not prehistoric but an interesting spot all the same.
There are similar but more ruinous structures over the road in the Sheffield Plantation on the Longshaw Estate.
There's speculation on other web sites as to whether the remains at Lawrence Field are actually of Neolithic origin. Their focus seems to rest on the one standing stone on the southern footpath being the single remaining standing stone of a possible circle. On my visit I walked west of that stone and thought that another collection of stones could potentially be the circle, especially as the accompanying structures seemed to tie in with the OS map reference to a 'settlement'. I'm writing up my field notes here so as to help people who're figuring out the truth from the speculation at Lawrence Field; there are many potential standing stones there that can easily lead you into false assumptions; I don't offer my speculations as any kind of claim to truth, as I could easily have been deceived by a random placing of stones, but this is what seemed plausible to me when I was there:
'This is potentially the stone circle in Lawrence Field. 5 stones in an oval (13 paces across), a couple at the centre (flat on the ground; a hollow area beneath them, special stones placed in there recently). All the circle stones are very low; 2 thin and side-on; one completely flat on the ground (but I'm presuming from its shape it was another flat stone standing side-on to the circle). A stone wall, mostly covered by earth/gorse, passes beside it. Which doesn't leave a lot to see of the stones and there isn't a particularly marvellous view of the landscape; but you can see a natural tower of stones poised atop an edge on one skyline [Mother Cap Stone]. I can imagine wanting to see that from your circle.
Off to the west, remains of a round structure whose walling seems too well preserved to be Neolithic. However there are two small cairn-like structures beneath a lot of gorse/earth and remains of two walls, one of which often uses upright stones.
Directly south of the presumed circle, toward the river, remains of three structures in a southward row. One appears to be a long cairn. A second is a similar elongated oval shape, but a little wider, and its a walled enclosed area. A third is a small round structure, buried under gorse.
To get here I took the path going south from opposite the 'Surprise View' car park on the A5187 (not far from Fox Houses, near to Sheffield) and half way to the trees found a smaller path heading west.
There's a lot of potential standing stones in Lawrence Field to confuse you.'