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The phrase "lower rate of" is correct and usable in written English.
You can use it when you are referring to the decrease of a particular rate or amount. For example, "The government has implemented a lower rate of taxes for small businesses."
Exact(58)
A lower rate of benefits for the under-21s.
Both these age groups have a lower rate of labor force participation that the general population".
Thelin showed a lower rate of side effects than Tracleer, Encysive said.
Movers saw a lower rate of change, at 4.7%, but paid an average of £286,000.
We are being told that they are seeing a lower rate of absenteeism".
Our pre-human foremothers probably had an even lower rate of reproductive success.
Confidence can lead to a lower rate of interest – but don't bank on it.
For example, the UK government applies a lower rate of VAT to energy.
"The lower rate of sterling makes UK food manufacturers very competitive.
"People are bidding up the purchase prices by being willing to take a lower rate of return".
He expected the trend to be reflected in a lower rate of growth in health spending in 2004.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com