Final answer:
The statement in the question is false. Many states were annexed to the British Empire through various means such as conquest, treaty agreements, and colonization.
Step-by-step explanation:
The statement in the question is false. Many states were annexed to the British Empire, not according to the doctrine of lapse of Lord, but through various means such as conquest, treaty agreements, and colonization. The doctrine of lapse was a policy followed by the British in India, where they refused to recognize the adopted heirs of Indian rulers and annexed their territories.