There are two runs in Alvor, a cute town just west of Lagos: a unique run on a series of wooden boardwalks, and the A Rocha Delicada paths around the estuary. The beaches are also runnable.
Boardwalk Run. ~5 km of boardwalks. This is one of the more unique runs in the Algarve. The Passadiços de Alvor is a series of wooden boardwalks that wind around the estuary and down to the beach. There are great views. There are about 5 km of non-overlapping boardwalks. There are two longer, east-west boardwalks (~2 km) that go from the parking lot to the pier, and two boardwalks that go down to the beach.
Beaches. The beaches in this area are a bit more runnable than in other parts of the Algarve, as there is some firmer sand near the water (tidally dependent). Alvor Beach is 3.4 km long, and Meia Praia is nearly 5 km long (they’re adjacent but not connected)