Before doing ghusl, I will put soap on my body, and then I will make niyyah to wash my body while the lather is still on. The soap doesn’t make a barrier to water, and I step under the shower and let the water wash off the soap.

Do I need to wash the soap off before I make niyyah for ghusl, or can I do niyyah for ghusl and then wash the soap off?

No you are doing it correctly. You can do the niya and then wash the soap off