HI EVERYONE, hope this helps,

Newcastle-under-Lyme city (1991 pop. 73,208) and district, Staffordshire, W central England, CLOSE BY ASTON
There's a small river called the Lyme that runs next to the A34. Newcastle is south of it, hence the name - Newcastle Under Lyme.
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under Lyne
There is some confusion over the origin of the "Lyne" element. A number of sources suggest that it refers to the place being under the line of the nearby Pennine hills. However, the name has only been spelt this way in modern times so this explanation seems unlikely.
One document of 1422 refers to the town as "Ashton sub Lima". Ashton later became known as "Ashton under Lyme". The name seems to have become changed to "Ashton under Lyne" by the time of the Victorian era.
It would see, then, that "Lyne" has been corrupted from the word "Lime" or "Lyme". According to various sources, the most likely origin of this "Lyme" element would seem to be from the ancient forest of Lyme, which at one time covered the uplands to the east of Southern Lancashire and Cheshire. The word "lyme" meant area of elm trees, and this would also be the likely origin of the names of Limehurst, Limeside, Lyme Park and even Newcastle under Lyme.
Other sources suggest that the "under Lyne" elements come from latin words meaning "within the boundary", indicating that Ashton was just within the boundary of Lancashire and before that Northumbria.
So, there is not one clear answer to the origin of the name, but it could well be the town takes its name from a house near some ash trees in a forest of elm trees!