We normally park west of the Haymarket Area (7th and P Street) and walk to the bars and to the stadium. It not paved and dusty so not ideal for tailgating.
I've heard that the paved lots at the baseball/softball complex west of the stadium have a lot of tailgating.
Then north of the stadium, over the railroad tracks is residential and many occupents sell spaces and tailgating goes on there.
Regardless of what you decide, alcohol is prohibited so any consumption must be in a plastic cup. Hopefully this reactivates your post and others jump in to help. There is a member of this board that sells space north of the stadium so maybe he can help out too.
Enjoy your visit to Lincoln!