When I was a paramedic we didn't learn lab values per se though we learned about the electrolytes, e.g. we knew what a low K or low hemoglobin meant, but we wouldn't have known that a K of 3.2 or and Hgb of 8.2 were low. Of course that was almost 30 years ago so they may get better training now. There are a few paramedic programs that give BS in EMS. Those are essentially like BSN programs but with EMS experience instead of bedside experience. As a medic I definitely would like to know what the patient's baseline vitals have been, what the monitor has been doing, any serious problems with labs, any serious problems with tests done.
For BLS (basic life support) transports they use EMTs not paramedics. They would definitely want to know vitals and any problems to watch out for but doubt the labs or monitor would be useful.
I find it funny that when some LTC facilities call us to take a pt to hospital on an emergency basis they give us the tranfer papers with all the patient info in a sealed envelope, feeling that we don't need to know the information. The envelope gets opened the second I get in the ambulance.