Is there a way to find and change uppercase letters of a certain character style and change them to lowercase within InDesign?
Yes! First, be certain the font has both upper and lowercase. Then, highlight the text you wish to convert. Locate from the top menu
Is this what you are asking?
If you need to find something specific you can try the Find/Change feature... Locate from the top menu
It will pull up a panel that looks like this... and with a little playing around, you can familiarize yourself with it's awesome abilities.
Other than by scripting, InDesign has no way to force lowercase in a global search/replace, as you have no doubt discovered.
A slightly-less-than-manual way to tackle this is by using
The automated part is to use a GREP search for any uppercase character in that Character Style. The manual part is to type the lowercase directly, overwriting the found character(s). Fortunately,