The parking lot is to the north of the football stadium. The baseball stadium is to the south of the football stadium.
https://goo.gl/maps/79drG
There appears to be a large parking garage in between the two stadiums.
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Nationals Park does have some nearby parking lots but most of those are temporary. The ones I saw were unpaved gravel, torn-up asphalt or grass, other than the parking lot that is part of The Yards development.
With development picking up pace in that area, many of those temporary lots could be redeveloped in the coming years.