I own a used BMW that was previously a leased vehicle and I can confirm from direct experience that I was able to ignore the scheduled service notification and

I own a used BMW that was previously a leased vehicle and I can confirm from direct experience that I was able to ignore the scheduled service notification and continue happily driving for thousands of miles with no issues. The car did nag me with a notification every time I started it up until I eventually brought it in, but I was fine with that.