Just to add to previous posts about Lenham Racecourse - I have found nothing helpful. We all found the greyhound article, but there seems to be little else floating in the ether. NLS maps have 6inch and 25inch of 1902/3 and later 1930s that show the field as "Old Race Course", but that's about it.
I even plodded through about 20pages of Hasted just in case there was an earlier reference to the course, but no luck.
Carry on regardless...