Lavender can be quite prescriptive as to when you prune and how much to take off. I have Hidecote and Munstead varieties (which I think yours is) and their growth pattern goes something like this (starting in Autumn):
Autumn - prune back stems and flowers, making sure you retain some silvery green foliage - if you cut away all the growth back to the hard wood, it could kill the plant.
Winter - the plant stays dormant, however in mild winters you may find it tries to lay down a small amount of silvery foliage.
Spring - growth is visible with the silvery toned foliage turning to vibrant green. Flower stems form with tiny purple ends.
Summer - stems continue to grow and strengthen and the flowers turn bright purple. If you cut these, you would not normally expect new flowers to replace them. I try to delay harvesting my lavender (for eye pillows, linen bags and to hang upside down in net bags in the wardrobes) as long as possible because the bees and other pollinators absolutely love the flower heads. I feel quite sad when I have to harvest them, it's normally in the chilly Sept evenings as the sun goes down, and the bees can get very annoyed at me!
Your lavender (left photo) looks like it's getting quite woody in the middle - if you carefully prune it this Autumn (as per my description above), by next Spring/Summer it will have a new lease of life. Right photo, I'd cut any of the brown flowers including stems, so the plant doesn't put all its strength into seeding and continues to flower for the rest of the summer,