Continued use of the same dripping for frying - is it advisable?
Firstly, I would challenge both of your assumptions.

(a) dripping doesn't go off

Like any other fat, lamb drippings can and will go rancid over time.

(b) any germs/bacteria would be killed by the heat of frying

While it's true that any molds or bacteria themselves will be killed by heat, the same does not hold for any toxins they may have produced.
Secondly, when you fry anything, you introduce small particles into the cooking fat. These will burn and -- health risks aside as they are off-topic for this site -- start ruining the flavour of the fat.
You can cook using animal fat rendered from lamb chops, or pork chops, or bacon, etcetera, but you should filter the fat, keep it refrigerated and cannot expect to reuse it indefinitely.