Is it safe for someone to sit on furniture and bedding if they have just been treated for head lice?

NO. The furniture should be wiped down and bedding washed to be safe.
Head lice. The person may have been treated but do they still have nits or lice? Vector transmission occurs when lice are spread through inanimate objects. For instance the lice can be on brushes, combs, hats, headphones, scarves, sweaters, coats, bedding, towels, upholstered furniture, carpet, stuffed toys & seats in a variety of areas. .
Head lice. Head lice if completely treated can no longer be transmitted to another human being.So , once treated, i see no reason why one could not use furniture.