Yes, he is typical. I had three sons. I found taking them to the park or beach/pool in the afternoon...they knew we would go would help them behave in the morning. My sons also had swim lessons which helped wear them out. You can do this with another mom who has children about your children's agae. As I had a relatively small back yard, we did this a lot. My youngest was also 5 years younger than the middle one.
Have a friend over for him. I know it makes an extra child, but if the weather is nice, they will play outside together. They do need this unstructured time. When it was rainy sons liked to play with army men...they would put them all over the family/living room and then shoot them with pellet guns that didn't hurt the furniture (depends how you feel about guns, but I found my sons made them of sticks so I gave up on the no guns since everyone in the neighborhood had them) Need to be checked on, but you can give your daughter some playdough or coloring paper while you work so she is not in their way.
Go to the library and pick out books for them. Read to them...it is not as tiring as chasing them, slows them down for a bit and Lilly should play on the floor or a play pen while you do this.
Have the older children play in bathing suits in the backyard with various strainers, squirt bottles, etc. or paint. Sidewalk chalk is fun.
Enjoy them...I know it is a rather busy time, but I miss it now:) Whatever you do, don't resort to the TV or computer. All children need active activities and time for being creative.
A few chores in the morning so they can help you be ready to get out in the afternoon also helps. Load/unload dishwasher, sort socks and underpants, fold towels, empty waste baskets,help you prepare a supper that just will need to be microwaved when you get home (I did this because we like to stay at the beach late and then I didn't have to cook afterwards)..a few things my sons helped with.
Enjoy this time even though it is very busy...my mom told me this when I complained to her one time...and she was right:) I miss doing things with them now that they are older. Time goes by too fast.