Can radiation from holding a laptop cause irreparable damage to your lungs?

No. There is no radiation given off by a laptop. There is no way to damage the lung or anything else in the body. Prolonged computer use on the keyboard with pressure on the underside of the wrist can lead to carpal tunnel syndrome.
Laptops do not make. Much, if any, radiation. Appliance (phones too) may produce low energy (very weakly penetrating) energy, and as we all know, heat. Thermal energy does not penetrate tissue very well, and as you know from your microwave, it takes time for the powerful wattage to heat up even leftovers. It would take a long time for ur laptop to defrost, and longer to ionize living dna.