The DLR website has posted a new map of possible future line extensions, which shows a possible route to Ladywell, Medusa, Catford and Forest Hill.
An extension south from Lewisham would require the abandonment of the current station and major work in the Lewisham area. As such, this route is still in the concept stage, rather than fully-developed, but it would add significant capacity to the public transport options in Catford, which suffers from relatively poor connections, and help to integrate it more effectively with the rest of the borough.
Despite the major challenges involved, the DLR has an impressive track record of delivering on its vision, so this map is more than just a pipe dream.
EDIT: Trainspotter found a reference in a document from 2005, which clarifies that an extension south of Lewisham would involve constructing new track, running in parallel to existing overland services:
South of Lewisham the proposed alignment is alongside and east of the Mid-Kent Railway
line. Some complex bridge works are necessary and there are tight alignment constraints at
Doggett Road, to the North of Ladywell Road, and on the approach to Catford Bridge Station.
Whilst some of these issues – together with the necessary modifications to Ladywell Station
and Catford Bridge Station – are significant; they are less critical than the interface near