Hello Dorothy,
Just a few thoughts :
Your predicament of trying to find a long gone village is one I've encountered but have been lucky to find the name was kept either in the name of a school, a tavern, a street name and once even a cachment area/ward - the name only used at election time. As the village name only appears in a family register, I wondered if it had been shortened e.g. my brother will tell you he lives in 'Thorn' but the village name is actually 'Thorngumbald' and my neighbour tells me he originates from 'Derry', but on the atlas it is 'Londonderry'.
Inputting 'Lahe' into the 'keyword' on familysearch brings up 3 entries, but doesn't mention Kreis Osnabr�ck. However, I recognised some names on the two which don't mention Hannover stadt as I am researching in the vicinity (west of Salzgitter, east of Osnabr�ck) and I've been told 'my' village/area was near a border - this means I have to approach various archives. The 'border' archive, I have been told, is Goslar. Have you looked at this possibility?
Rena in England