I must admit that my first impression of the lawn agrees with BB's post that there looks to be a lot of shade from trees & that retaining wall. The large tree in the middle of the front lawn adjacent to the path is going to cause issues with getting the maximum density from the grass.
With regard to scarifying I always have the opinion that any time is a good time providing the grass is actively growing. If there is a thatch issue then I would say it is better to correct that issue as that will impede water and nutrients from reaching the roots as well as providing a haven for pests and disease. That being said if you do proceed with either a hard scalp or a scarify you must nurse the grass back afterward with a bit of love, namely with water and fertiliser.
Do you have an irrigation system installed?
