I owned a 2012 LaCrosse, and my iPod classic worked well with that car, but there were some occasional hiccups when the iPod would stop working, and the only way to get it going again was to reboot the iPod.
I just took delivery of a 2019 Lacrosse and was very disappointed to have encountered this problem. I tried some of the suggested solutions, but kept getting the same results – the iPod would work for awhile (about 2 to 5 songs), then quit, and my screen would report that there was “no media.”
The only workaround I’ve tried with any success is to connect the iPod classic to the 3.5mm input, and plug it in to the outlet in the compartment using a USB adapter to keep it charged. The solution is not very satisfactory, however, because you can’t select, skip, pause or stop anything using the audio system’s controls – only the iPod wheel can be used for this.