Best thing to do is call the Parks dept. Or you can call the City of Arlington and they will get you in contact with right dept.
Parks & Rec department is who you contact if you are planning a major event, i.e. inviting the public for a group sponsored event then best to reserve a pavilion / amphitheater, etc. So that you'll have the proper permit/s, (wedding, cos-play event, large family reunion, production, etc) If you're just wanting to have a simple family or friends get-together or cookout then just show up (first come first serve ).
It's $100.00 to rent the pavilion
Just call the City of Arlungton and they can put you in touch with the right dept. that handles that .
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