I'm not familiar with the Lisa Widget drive, but a lot of drives of that era had head stiction problems. The heads would stick to the platters when stopped, usually at the edges of the working surface where the heads sweep the lubricant. Though the brakes release, the disk fails to spin because the heads are stuck in deep gooey lube. The rising and falling pitch is the motor start circuit pulsing the motor coils at various frequencies to try to break it loose. A close listen, or if you can see the brake drum, will tell whether the disk is actually spinning or not. If the disk is actually spinning up and slowing down, the drive is having problems reading the sync signal embedded in the data tracks. In either case, there's not much you can do about it without access to a clean room and a good supply of spare parts.

One thing you can check is the power supply voltage. If 5V or 12V is off by more than a half Volt or so, that could cause flaky operation. Hope you can get that Lisa going.