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.
Richard Lindzen did not win the Nobel Prize. He is a prominent atmospheric physicist known for his research on climate dynamics and atmospheric physics, but he has not been awarded the Nobel Prize.
Richard Kuhn won The Nobel Prize in Chemistry in 1938.
Richard Axel won The Nobel Prize in Physiology or Medicine in 2004.
Richard Martin Willstatter won The Nobel Prize in Chemistry in 1915.
Richard Adolf Zsigmondy won The Nobel Prize in Chemistry in 1925.
Richard E. Taylor won The Nobel Prize in Physics in 1991.
Richard R. Ernst won The Nobel Prize in Chemistry in 1991.
Richard E. Smalley won The Nobel Prize in Chemistry in 1996.
Richard R. Schrock won The Nobel Prize in Chemistry in 2005.
Richard F. Heck won The Nobel Prize in Chemistry in 2010.
Richard P. Feynman won The Nobel Prize in Physics in 1965.
Richard J. Roberts won The Nobel Prize in Physiology or Medicine in 1993.
The Nobel Prize in Chemistry 1938 was awarded to Richard Kuhn for his work on carotenoids and vitamins.