...wouldnt the vapour still escape when you take off the cover?...
Not really. Once the lye solution cools a bit, the mist no longer forms and there's nothing that wants to escape.
Think about a cup of hot coffee or tea -- at first you can see mist rising in curls from the cup, but after awhile, the mist stops. Same thing with hot lye solution. It only takes 10-15 minutes for the mist to stop.
After the mist stops forming, you still want to keep the lye solution covered but at this point, the need for a cover is not to control mist escaping to harm a person. It's about minimizing the loss of purity as NaOH reacts with carbon dioxide in the air and reducing how much water vapor the lye solution is able to absorb from open air.
Most soap makers don't realize the concentrated lye solution we use for making soap will generally absorb water from the air and thus will gradually increase in volume. We're used to plain water which behaves exactly the opposite. The only time a soap maker's lye solution would lose water to evaporation and decrease in volume is in a place like the deep desert where the relative humidity is super low.