I had a quick spin down the Witham area last week and had a look at those earthworks while I was there. First thing I noticed was that I was looking in the wrong field (I think), on the map link you posted- http://www.multimap.com/map/ph[...]ang=&db=pc&coordsys=gb
I was looking in the field slap bang in the centre of that photo and couldn't see anything. Turning round and looking south there were indeed a load of earthworks in the field between the road and Barlings Hall. They looked pretty waterlogged and not that ancient either. Checking back to the map and zooming it up a notch- http://www.multimap.com/map/ph[...]&down.x=259&down.y=324
in the top half of the photo it looks like the ground plan of some kind of hall or other large building, although the earthworks might suggest a moat or some serious drainage problems – maybe it was a giant fish pond! It does actually appear on the edge of that plan I mentioned previously but my money is on it belonging to the abbey or even something more recent but a quick word with the bods at Lincoln museum should sort it out.
I'll say one thing though – it's nice round there isn't it :-)