The entry you found on the DAR Patriot Ancestor index appears to be lifted right from his pension application.
This was pretty common in older DAR members' applications, ignoring any service records that may have been harder to access.
Surviving rosters for Lee's Legion are in National Archives Micropublication 246, "Revolutionary War Rolls," microfilm roll 115.Rosters for the 1st and 2d Light Dragoons are also on this roll.You can ask your local library's inter-library loan dept. to borrow this for you to look at.If your library subscribes to ancestry.com you can also browse the digitized images.
Both ancestry.com and footnote.com have the Compiled Service Records for individual soldiers which the War Dept. extracted from the above original documents (making a card for each entry).On footnote.com the extracts are indexed.On ancestry.com you can only browse by Regiment.
You can look at a fairly good compendium of data on Continental Army officers in F. B. Heitman's /Historical Register/, here: