If your Gt Uncle was sent to Blencathra Sanatorium from Gateshead, after he died he may well have been taken back home for burial. I have researched a small number of people who died at Blencathra Sanatorium and they were buried in a churchyard near their home rather than Threlkeld Churchyard.
Ideally, the next step would be to check one way or another whether or not your Gt Uncle was buried in Threlkeld Churchyard. I understand the Burial Register for St Mary's, Threlkeld is still with the parish and with no copy in the County Archives.
If, on the other hand, the County Archives does have a copy of the Burial Register you could ask someone who is a regular visitor to the Archives if they could do a 'look up' for you. If your Gt Uncle is not buried there, then you would know to look around Gateshead for the burial location.
Good luck.
(Photograph of Threlkeld Churchyard attached)