Not sure about elsewhere, but here in Australia CAR 249 states that
"...an aircraft that carries a passenger shall not engage in any of the following types of flying:
a) Flying training given to a person who has not passed a general flying progress flight test for aircraft of the category concerned
[categories being aeroplane, helicopter, gyrpolanes and airships].
b) practice of emergency procedures in the aircraft
c) low flying practice
d) testing an aircraft or its components, power plant or equipment" [unless a maintenance engineer is required as part of the test flight]
So no, you can't carry passengers on a "trial lesson" in Australia.
Elsewhere if there is no definitve regulation it would be worth checking with your insurance company to see if passengers carried on training flights were covered if something went wrong, or if they could sue the pants off everyone involved. I believe in the UK this is often covered by those passengers becoming a temporary member of the club.
Anyway how many 'legit' studes would want their friends or family witnessing their lesson?! *cringe*