You want 'natural'?
You'd rather shave off all of somebody's hair than use 'a chemical'? If it makes you feel better, the most popular agent to kill lice
over the past 50 years (pyrethin) comes straight from chrysanthemums (pyrethin 'mum' in the picture).
You're wise to be suspicious of artificial chemicals, but in this case, I think your fears are misplaced. I hope your treatment proves effective. Best wishes.