Final answer:
Queen Elizabeth, I passed the right to claim land in North America to Sir Walter Raleigh after Sir Humphrey Gilbert was lost at sea. Raleigh established the 'lost colony' of Roanoke in 1584.
Step-by-step explanation:
The queen who gave the right to claim land in North America was Elizabeth I. Queen Elizabeth I of England granted Raleigh a charter, authorizing him to establish a colony in North America. This was in 1584, during the reign of Elizabeth I. Raleigh's expedition led to the discovery of the Outer Banks and Roanoke Island.
Initially, this right was granted to Sir Humphrey Gilbert, who was lost at sea during his third voyage to the Americas. Following this event, Queen Elizabeth I passed on the grant to Sir Walter Raleigh, Gilbert's half-brother, in 1584. Raleigh led an expedition that founded the first English colony in North America, the 'lost colony' of Roanoke. Therefore, the correct answer to the question is Option 1: Sir Walter Raleigh.