I have two hurricane lanterns which burn parafin and was planning to use them when we go camping in our bell tent in a few weeks. Due to recent story in the news about family in Wales I am getting a bit worried about the safety of using the lamps inside the tent.
To be completely safe, don't use them. However, if the groundsheet isn't either sewn or zipped in then there should be pretty good ventilation, especially if there's also vents at the top so you can get some circulation going and fresh air drawn in. IIRC, CO is only going to be produced when levels of oxygen are insufficient to allow the burn process to generate CO2 - good ventilation will both allow enough O2 into the tent to ensure the lamp burns efficiently (and doesn't make CO to start with), and allow exit routes for any less desirable fumes that are produced.
But if you don't want to take a risk, don't use them in the tent at all.