Can an employer, by law, require that an employee take the work lap top and perform job functions while on vacation?
Can the employee be terminated for refusal to do so?

Neither federal nor any state law that I know of has protection for work ordered to be done while on vacation.
If your company publishes their own policy and it's stated in there, then you have a case.
This is the sort of situation that you have to handle using all the brains and finesse you can muster. Either your laptop won't pick up a signal, it gets full of sand, or you just flat out refuse, or charge the boss with hours worked against future vacation time. Figure it out.

Yes, you can be fired. A vacation is a perq, not a hazardous work condition or overtime or denial of a break to use the bathroom.

Do you have a contract with the company? Are you a salaried employee?

It also depends on your job. They may, legally, require that you check your mail and be on call. But then you may be able to negotiate something in return.

You can of course turn in to be paid for work time.