Is an SSD required to run a bitcoin full node and a lightning node?

A SSD is not required for running Bitcoin, but it certainly helps. You would definitely want one if you were running a production service using Bitcoin, but for something you’re using personally it will just make synchronization substantially slower to use a hard drive. For a Raspberry Pi you absolutely do not want to be storing any data on the micro SD card it uses as a boot disk, as this will result in corruption at some point.