Not real familiar with the maker or the exact time frame, mid to late 60s? Some info here http://www.racingfromthepast.com/lavernnancehomeindex16.html
Yes 16" dirt track tires were most common in the time frame that that wheel would have been made. I got to ask are there any markings on the back side? Most Nance sprint car wheels were pin drive by the way, the dual pattern makes me thing that these are not pin drive.
Most of those fellas back then were pretty proud of their product. The 6 windows pretty much rule out most wheels, could be that they are drag masters like has been mentioned.