Hi PJSim...yup, everything on that lot will move with it. I had a large house with a big patio in back for my lil party sim and her husband had the green thumb. There wasn't enough room for garden expansion as his skill in gardening grew. I think their lot was a 30x30, so I looked around and found a 30x40 and just moved the entire lot.
You just have to make sure the lot is facing the right way. I had to extend the sidewalk to reach the street, but yeah, everything moves with it.
Daniel now has a very large and lovely garden.