After the bars are cut and curing its not lye fumes that are a concern. If the recipes use lots of EO or FO its not recommend for someone with breathing problems. If you are allergic to ragweed, I wouldn't sleep next to some curing bars that use chamomile EO. During cure the EOs are evaporating out of the soap.
The curing issue lies in the scent. I remember that somebody was complaining from headaches from curing more batches of heavily scented soap in the same room.