lay claim to 権利を主張する

lay claim to は所有権、権利を主張すると言う意味です。 0:01 it's the first time any legal challenge has been brought in the South China Sea territorial dispute, both China and the Philippines lay claim to the reefs, rocks, artificial island chains in the area and their surrounding waters.

South China sea dispute: UN court rules China has no 'historic rights' to South China Sea resources
https://www.youtube.com/watch?v=Nu8jaTD9370  3:42 no less than 6 American towns and cities lay claim to the title. アメリカ海軍の発祥地として少なくとも六つの市町村が名乗りを上げている。
5 Things You Don’t Know: U.S. Navy
https://www.youtube.com/watch?v=LlB-EKm4HNk  0:42 an adult male has already laid claim to a dead Beluga washed up at low tide. 浜に打ち上げられたシロイルカの死骸は雄のホッキョクグマが独占していた。　
Polar Bear Carcass-Eating Etiquette

練習問題解答
a-3820 lay claim to
b-3713 lays claim to