Near the house you have some parks like the park from Museu do Trajo where you have a 60 m tall araucária.
Is a nice place in very hot days.
It is near Golf of Alcoutins.
Near the Ameixoeira Metro Station you have an small park.
For runing and jogging the Quinta das conchas has a 3 km perimeter and is at a little more than 1 km from the home.
Here you can see an aerial photo of the area.
Lisbon has many other parks where you can go.