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I know this lady who makes a lot of money (a lot) and she works very hard for it. With her well earned money she buys herself huge (huge) diamond rings, goes on many vacations, buys the best clothes, and has a few cool cars. Now she's looking to buy a lake house in addition to her 3000 square foot house overlooking the river. She says she's frugal because she lives below her means, not getting into debt at all. Does "frugal" apply in this case? Does being frugal mean you're always budgeting for groceries or having to save for the smallest luxuries?

"Frugal" can be living within ones means. It is very hard for people to understand different economic classes. Just because someone is rich doesn't mean they are smart with their money. There are people that make over a million dollars a year, but spend it in stupid ways and still live paycheck to paycheck.

frugal is living with in your means!
if your living pay check to paycheck then you should re do your budget to live with in your means is equal to
i do not spend more then i make!
weither you make 5 dollars a day - 5,000 a day that's how class and stuff is made!

Well, there is an operative assumption that if the "Rich" (practically defined as anyone deriving most of their income from dividends or stock portfolios), they are taxed quite differently from someone receiving a w2.
The average taxpayer earning under 200k pays - without deductions - about 35% of their income towards taxes.
Nearly 65% of the net wealth of our nation is "owned" or controlled by 1% of 1% of our population, or a little more than 50,000 people.
THESE are the people you would most want to tax, and right now, they pay around 5-10% and never more than 15%, and if their financial advisers are doing their jobs, usually they pay nothing at all, save the fees towards their advisers.
It might be nice to suggest these are the "wealth generators" , but that's not the case, the majority of the "working wealth" year over year, is consistently created in the small business arena, the lower, middle and upper-middle classes.
How this helps the "middle" class is that currently , our wealth as a nation is seriously over-concentrated, in the hands of a few tens of thousands of individuals. In the macro-economic sense this is NOT healthy for a commercial / political system because that wealth is NOT reinvested and is essentially sequestered off from the active economy, in structures which do not give access to capital to the broader marketplace.
Taxation is an effective means to redistribute the wealth concentrated in that upper echelon of our society, but don't worry, our friends at Fox and elsewhere will fight extraordinarily hard to convince everyone else that - it's in their interests - to not over-tax "rich" people.

I know a lot of people with a considerable amount of wealth and they are still frugal. Funny eh?