When did Richard Lindzen win the Nobel prize?

He didn't. Well maybe kinda. When Gore one the prize back in 2007, every author and contributor to the IPCC report was included in the citation and in some circles this is regarded as "being awarded a Nobel". I believe Lindzen was a lead author on one of the IPCC volumes.

This is the same basis on which Monkton - who commented on aspects of the report - has claimed to be a "Nobel Winner"

This however, ignores the fact that only a maximum of 3 authors can claim the prize. There were over 2000 on the IPCC report.

So short answer - Gore got it. About 2000 others - including Lindzen - got "mentioned in dispatches", but no they didn't win it.