If you are lucky enough to live close to a beach, or lake, then swimming is the best form of exercise, especailly for puppies. You can also divert attention and increase your dogs enjoyment by alternating between swimming and digging.
You need two floating toys, and a jar of Marmite or peanut butter. (But be warned your hands will be a mess! Just wash them when you are done in the sea or lake)
While your dog is in the water bury a float toy (lightly smeared with marmite (or yeast extract), sometimes peanut butter) in the sand. When your dog comes out of the water simply tap your foot at the recently buried item and let him start digging. Give loads of encouragement to start off, but he will soon work out the game.

Once he has discovered the booty he will want you to throw it into the water, (forgetting about the float toy he has just taken from the water.)
The secret, if there is one, is not too smear too much on the buried toy, otherwise - as I have found, he will happily swim around for ages - enjoying both the swim and the taste of the toy!
After a while you will work out just how much to smear on - to get them to dig, and just how little to smear on to stop them for staying too long in the water.
All dogs love routine and can quickly work out the game. Swim, dig, swim, dig, (by ten) is what you are looking for. Eventually they will tire of pleasing you and themselves, and it will be time for home! Both you and your Lagotto will have had a great day out and your dog will expect the same game the next time you go to 'his' beach or lakeside.