Holding a pet in your lap is not safe. In an accident or even a sudden stop, the pet will go flying. IMO, a hard sided pet carrier buckled into the back seat is the safest place for an animal. We've had this discussion numerous times on the old forum and if you do a search you can probably find the threads about it.
Proper pet carriers are readily recognizable by emergency personnel as containing a pet and they will take appropriate actions. Soft sided carriers, lunch box carriers and purse style carriers would usually be overlooked in an accident as they don't look like carriers.
Hard sided carriers also protect the pet from any flying objects in the event of an accident and being ventilated on all sides ensures there is still ventilation if one or more of the sides gets blocked.