The amount is less/lower by 1000 US dollars

Which of the following below is idiomatic?

The amount is less by 1,000 US dollars.

The amount is lower by 1,000 US dollars.

Neither. Either sentence would be improved to become natural English by placing the comparison after the price:

The amount is $1,000 USD less.

The amount is $1,000 USD lower.

Though, which you would use depends on the context of the conversation / writing. Also, I changed the dollars to be consistent with English usage. While technically 1,000 US dollars does describe how many units of what type there are, the standard for writing this is with the dollar sign ($) and then the USD following, which is the financial indicator for U.S. Dollars.