Perhaps what you meant to say was that Lloyds doesn’t meet some requirements of the Affordable Health Care Act, or that your physician doesn’t accept them for direct payment… but I assure you they will write a catastrophe policy, and you can claim, and they will pay anywhere in the world, including the United States.
Not only that, but they have done so reliably for hundreds of years.
Also, many high net worth individuals save money with what’s called a catastrophic policy.
Very inexpensive premiums, with a very high deductible. Day to day they pay out of pocket and save money. The policy would cover catastrophes such as cancer or a major heart issue.