He wouldn't have a middle name at such an early date. The widespread belief in 16th, 17th and early 18th century "Richard Henry" Lees are ALL because of the Richard Henry Lee celebrated in the musical "1776". (That and the inability of many moderns to wrap their heads around just HOW modern middle names really are.)
As to the baptismal date, I tossed it. We don't even *have* an actual baptismal date for Richard "the Immigrant" Lee - the record, if there ever was one, has been lost. Even his birth date is a guesstimate and could have been earlier - say c. 1610.
As to his actual parentage, that's a hairy and highly contentious subject. At present there are two or three sets of names in the hat, each with arguments for and against.