Tony,
I have just had a quick look at a LG DVD Recorders' manual (DRT389H) and this particular one can record onto DVD+R DL discs. ie Dual-Layer discs that match the DVD+ specification. (It doesn't mention anything about DVD-R DL.)
However the problem is that these are write-once only discs. They cannot be reused to allow you to record 'over the top of' any programmes that you have already recorded on the disc, have viewed and have finished with, like you could do with a VHS tape. (Or as you are probably already doing with a rewritable DVD Disc such as a DVD+RW, a DVD-RW or a DVD-RAM.)
I don't believe that blank rewritable dual-layer DVD+RW DL or DVD-RW DL discs are available for purchase.
Taken from a wiki article:
A dual-layer DVD+RW specification was approved in March 2006 with a capacity of 8.5 GB.
[2] However, manufacturing support for rewritable dual-layer discs did not materialize due to costs and expected competition from newer formats like
BluRay and
HD DVD, which boasted up to 25 GB on a single layer.
DVD+RW - Wikipedia, the free encyclopedia
I reckon that you will have to stick with your current non dual-layer discs if you want to reuse them like a VHS tape.