There was a big grassy area in the park I went to and lots of people were laying down relaxing there.
この場合、次のような言い方ができますよ。
ーThere was a big grassy area in the park I went to and lots of people were laying down relaxing there.
「公園に広い芝生のエリアがあって、たくさんの人が寝転がってくつろいでいた」
a big grassy area「広い芝生エリア」
to lay down relaxing「寝転がってくつろぐ」
ご参考まで!