Do they make a ventless toilet? My friend has installed a new toilet and learned after that the previous owners didn't install a vent on the drain.

Do they make a ventless toilet?

No... not a toilet that will install onto real plumbing. Your friend may be able to install an AAV (air admittance valve.. see pic.)) close by.. but will still need to cut into the plumbing to install it.

How is it that they know for sure no vent present... In fact, if lavatory sink is next to this toilet the lavatory may be acting as a WET VENT for toilet..and that is permissible everywhere..?

Let me know what you think... Mark