Lyme is usually a bull's eye rash. I am sure you have seen pics on the net. A lyme bull's eye to me looks like a bug bite, but with a definite ring pattern.
Lupus is more of a rash, like a baby heat rash and it is as you describe - butterfly across the nose and on the cheeks.
He should see a doctor. Since you suspect lyme and you think his symptoms coincide, maybe find him a llmd.
Here, give him this test to take.
lymeontario.com/wp-content/uploads/2015/03/Horowitz-Questionnaire.pdf