A lav mic is probably not the best idea, because they're omnidirectional and they pick up everything around then. The voice would surely be louder, but the machine is close enough to bed picked up by the capsule anyway, without mentioning all the sounds of her hitting the microphone inadvertently every few seconds, which is quite likely in that context.
An hyperdirectional shotgun mic is probably better, but that would require her staying in a single position for the whole video, or someone manually pointing the mic towards her mouth, and pretty close at that.
Unfortunately there's no miraculous solution that would help here. A quieter machine to start, professional cleaning software, and some paid stem separator are the only way to get rid of that sound.