I expect they're both sources of the Dour although Drellingore is three miles away from where the two sources meet. I've just been looking at a Bygone Kent which shows the lake at Drellingore, I also have some photos of the river running down through the Alkham Valley, I'll scan them later.
I wonder how often the river would break surface if the pumping station at Drellingore were 'switched off'?
A Mr G Gough carried out a survey in 1956, his report is at Dover Library, in it he mentions the various sources, Lydden Valley, Alkham Valley, Poulton Valley, Elms Vale and the old spring at Ladywell. These are mostly dry valleys now due mainly to extraction by water companies.
The pond at Drellingore, he states is fed from a spring a bit further up the valley at Chilton from where water flowed almost constantly, (this was in 1956).