Hi!
Well the lever is required to let the ribbon cable work. Without the lever the cable won’t make (good) contact and thus the fan won’t work.
So, yes the lever is required to be intact to let the fan work.
For now, I would replace that one (this won’t be easy as you need to (micro) solder now.
When this is replaced, it should just work. If not, you need to test some resistors and capacitors on the motherboard.
You can also choose to replace the whole motherboard. Way easier, but way more expensive..